I need help, I want to trick a digital camera for use in a power supply without batteries, because of the batteries can survive less than 5 mins.

What can I made for trick the camera and work with a power supply?

First most cameras have 5VDC supply input on some connector, usually asking for 2A rating. So connecting any 5V/2A "mobile charger" to that connector should work.
Otherwise:
What batteries it takes?
If R6 (I guess so from your photo), you may count anything in the 1.1..1.5V per cell, round it to the nearest convenient voltage for an available regulator.
If it is a LiIon cell, 3.3V should be OK (if the converter is adjustable, you may set it to the 3.6 or 3.7V, anything within the 3.2..4.2V range should be fine)
Industry standard voltages are 2.5V, 3.3V, 5V, many convertors are actually adjustable.
Then use some DCDC step down converter module (E-bay, AliExpress, Banggood,... are full of these), rated for at least 2A output and set or settable for the voltage you need for the camera (see above). Place this module into the battery compartment and connect instead of the battery, with input wires going through the battery cover.
Then supply this from some 12V or so of suitable power rating (count the module efficiency as about 60%).

For 5V you may use directly some 5V brick, then you need an low ESR capacitor (in the 1000..2200uF range, rated about 10V) placed in the battery compartment in the camera to eliminate the inductance of the cable.
Using the converter has an advantage in the possibility to supply its input directly from the car 12V socket...

My camera uses 2x 1,5V AAA battery, and I tried to give "the same voltage" with a resistor but not work.

My camera uses 2x 1,5V AAA battery, and I tried to give "the same voltage" with a resistor but not work.

This can never work at all. Cameras are equipment, which varies its current consumption from zeto to amp range bursts within 10's of microseconds. So a resistor in series means the voltage would be way too high (to even cause some damage) when the camera draws nearly nothing and drops to zero (so the cameras computer collapses) once the camera attempts to draw some current.
The peak power demand uses to be in the 5W range, it i just in a short burst (the time when the image is processed), it is tge main reason why they are so demanding on the batteries, mainly the "3V" types (mainly on their internal resistance).
The voltage should all the time stay within the cameras limits, the power source should maintain that even with the current varying so much. The thing is designed for batteries with some small internal resistance connected only by few cm wires (the internal wiring from the battery sockets to the power management circuit), so you need something to mimic that very closely.
That means it can not be connected by any long wires (their inductance is the main problem, so the need for either the main regulator module or a low ESR capacitor in the milifarad range (2200..10000uF) immediately inside the battery box, so then thehigher inductance of the wires is not that big problem (the regulator allows way greater room for the voltage variations on its input, the cpacitor takes over the fast current changes and so the current becomes more smoother on the upstream wire, so in both cases the system can tolerate a reasonable wiring there.
Personally I would recommend the regulator module (there are many 2..3A adjustable switching regulators on ebay, ali or so, with a form factor suitable to fit within the 2xR6 battery compartment, because all you need then is just some rough 12V (read as: Including the over/undershoots on the cable inductance anything between 6..30V, assume the thing uses somecommon 36V automotive rated chip, such as LM2596 or so; they are dirt cheap now, so loved by those cheap DCDC module makers)

I wonder what moron designed that camera. In addition to the 3 minutes of life the camera drains 300uA which is unnecessary, my LCD clock just needs 4uA to work, so if you leave the batteries on the camera they will die in some days. Also, if you take out the batteries for recharge them or replace them you will always lose the current time and date and it will reset to 2013.

That camera design is purely moronic, specially the last one, Is it that difficult to add a capacitor or battery to keep the clock?

I wonder what moron designed that camera. In addition to the 3 minutes of life the camera drains 300uA which is unnecessary, my LCD clock just needs 4uA to work, so if you leave the batteries on the camera they will die in some days. Also, if you take out the batteries for recharge them or replace them you will always lose the current time and date and it will reset to 2013.

That camera design is purely moronic, specially the last one, Is it that difficult to add a capacitor or battery to keep the clock?

It then seems the camera does not have any dedicated RTC, but uses the 32768 clock (maybe divided a bit) to periodically wake up the main processor to count the time. But still: Most processors contain programable divider for the 32768 clock, so it does not have to wake up that much often, so average consumption within 20..30uA, with a capacitor backup for battery replacement should be possible even without any dedicated RTC.

That's what happens when you let the morons or underpaid engineers to design your product just for save a few bucks. I think that an extra capacitor, battery for not to loss the time when you retire the batteries are not much extra cents per piece, or a dedicated rtc that drains the battery more slowly, just by investing few tenth of cents per piece will considerably improve your product.

I just have to ask. Can a quartz clock circuit be used to supply the time and date to the camera? Quartz clocks consumes ridiculously low current, my LCD clock drains 4uA from the battery, and without LCD the clock should drain about 1uA, which would last for around 100 years if the batteries don't start leaking first. My clock counts seconds, minutes, hours, days and months, so adding a year count shouldn't add too much current demand, so all should be draining about 4uA from the battery including a flash memory for saving the settings.

BTW do you have an schematic of a quartz clock?

That's what happens when you let the morons or underpaid engineers to design your product just for save a few bucks. I think that an extra capacitor, battery for not to loss the time when you retire the batteries are not much extra cents per piece, or a dedicated rtc that drains the battery more slowly, just by investing few tenth of cents per piece will considerably improve your product.

I just have to ask. Can a quartz clock circuit be used to supply the time and date to the camera? Quartz clocks consumes ridiculously low current, my LCD clock drains 4uA from the battery, and without LCD the clock should drain about 1uA, which would last for around 100 years if the batteries don't start leaking first. My clock counts seconds, minutes, hours, days and months, so adding a year count shouldn't add too much current demand, so all should be draining about 4uA from the battery including a flash memory for saving the settings.

BTW do you have an schematic of a quartz clock?

There is no need for extra quartz clock, the camera processor is able to do it as well. It just needs reasonable programming.
The 32768 par with its dividers is in fact just a stripped down circuit from a quartz clock.
The key is to not wake the main CPU that often. And after wake, use only the internal RC clock for the CPU, so you dont have to wait for the main crystal oscillator to run up. And program that routine so it does really minimum processing there (just increment the real time variables) and then go to sleep again. If you wake it about once per minute, it is enough to keep the time correct on the next turn on (it may then start 1 minute off, but with the next interrupt from the 32768 counter it becomes back spot on). That way you easily get to the uA as well, without extra HW. Of course, the power management should be of a low power type as well (in fact that would be the largest consumption contributor, but still the total 20..30uA should be feasible; that is more than 6 years of standard R6, assuming the cell itself wont degrade over that time).
Even your 300uA should make your batteries last for at least half year there.

Other thing: NiMHs tend suffer from rather high selfdischarge, it is not uncommon to have them flat after barely two weeks. Mainly when they have seen high current usage (that is, what the camera does to them) or when using fast, high current chargers.