I am trying to power my Arduino Uno with 9V, 500 mA AC/DC adaptor, but my controller will always reset after 3-5 minutes. As far as I understand 500 mA is too much?
Could you please suggest the salvation?
Tell us what you have. Which Arduino board, which controller, what else is connected, and so on.
Is that a regulated 9V ? Do you have a multimeter to measure the voltage ?
If the 9V is not regulated, and it is 14V instead of 9V, then the voltage regulator on the Arduino board could get too hot, and it shuts down.
Which device is reset ? Perhaps there is a ground problem that causes the reset.
That is Arduino Uno R3 with LCD display, photoresistor, buzzer, DHT11 and soil moisture sensor with MOSFET relay.
The power adaptor label states it is 9V and 500 mA.
The board itself shuts down.
I never measured the voltage of that adaptor, but now I did: 15,91 V. Never trust the label 
15,91V ! That is the open voltage I assume. Perhaps with the Arduino and the display, it will be some lower.
The backlight of the display requires some current, the voltage regulator will get hot very quick.
If you put your finger on the voltage regulator of the Arduino Uno board, you should feel it getting hot.
Can you get a regulated power supply of 7.5V (or 9V) ?
Note to OP.... what you said in your opening post, indicates that you think a 500mA supply will force that current on the device. That's not true: it's the maximum it can supply, and nearly all devices will just draw the current they need. As long as the ask is less than the maximum, which is what the label on the supply tells you, you're good.
If that was not the case, we would melt everything in our homes since the national mains supply has huge capacity, and our 100W lamp would be forced to take GW.
If you are going to get an actual regulated supply, get a proper 5 V (1 A) switchmode one and feed it directly into the 5 V terminal on the Arduino.
Thanks! will try to get a proper one adaptor.