How to build an LED dimmer on esp8266 using IRFZ44N?

I would like to build an led strip dimmer based on the esp8266.
In the circuit I have available voltages of 3.3V (esp8266 power supply), 5V (relay) and 12V (led power supply).
I managed to connect the relay via a PC817 optocoupler and a BC547b transistor - it works.
The leds I wanted to control via PWM. The written code is ok - when I connected the diode directly to the esp I got a dimming effect. I wanted to dim the tape with the IRFZ44N. So I assembled the PC817 -> BC547b -> IRFZ44N circuit. Unfortunately I did not get the dimming effect. At some point the strip lights up with all the power.
Could someone more experienced give me a schematic or at least some guidance?

My first thought was to do it on a BT137 triac, but the led power supply only lights up the strip a while after it starts up - probably stabilising something before it starts up. I was afraid if I would damage the power supply that way.

I have little experience in electronics so would appreciate any suggestions. Of course, I will share the source code and schematics once the project is complete so that the next one will be easier.

You only need one proper transistor, e.g. IRLML6344, which you can control directly from the ESP8266. Plus 2 resistors - from the ESP8266 output to ground, e.g. 20k, and from the ESP output to the transistor gate, e.g. 1k.

It is impossible to find the error in your solution, because you have not shown the schematic.

I won't be able to attach the diagram until tomorrow.

I understand that the transistor you suggested would be the best and most convenient to use, but will I be able to get the desired result using the components I already have?

You must use any "Logic Level" transistor, i.e. certainly not IRFZ44. The transistor should be specified for a gate voltage of 2.5..2.8 V (i.e. it should have RDSon at this voltage in the parameter table).

Thank you for your interest in the topic. Would STP40NF03 or IRLU024N be suitable?
I still have a question about the power supply - I wanted to use a 5V charger for my phone. What is the best way to switch to 3.3V?

Take a look at the datasheet and see if it specifies RDSon for VGS below 3v and what this value is. If it does not exceed 100 mOhm - it is adequate.

It seems to me that the STP40NF03 will be ok:

Any progress with the layout?