This is a very easy build for about 20 - 25 €
Components
1×
Pi Zero 1.3 - 5 €
https://www.kubii.fr/fr/pi-zero-v13/1401-raspberry-pi-zero-3272496006973.html
1×
a mini-HDMI to HDMI cable - 2 €
https://www.ebay.com/sch/i.html?_odkw=mini+hdmi+to+hdmi+-adapter&_sop=15&LH_BIN=1&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR11.TRC2.A0.H0.X%22mini+hdmi+to+hdmi+cable%22.TRS1&_nkw=%22mini+hdmi+to+hdmi+cable%22&_sacat=0
1×
A Pi Zero box - 1 €
https://www.ebay.com/sch/i.html?_from=R40&_sacat=0&_sop=15&_nkw=case+pi+zero&rt=nc&LH_BIN=1
1×
USB Gamepad - 4 €
https://www.ebay.com/itm/161716331843
1×
Micro USB cable - 1 €
https://www.ebay.com/sch/i.html?_odkw=pi+zero+hdmi+usb&LH_BIN=1&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR12.TRC2.A0.H0.Xcable+microusb+usb.TRS0&_nkw=cable+microusb+usb&_sacat=0
Beware, Pi zero has 2 micro USB ports : one on the right for power, the second (between the other micro-USB and micro-HDMI port) for USB device like the gamepad (or a keyboard).
Connect :
1/ the HDMI cable to your TV, 2/ connect the power cableto your TV (or to a power adapter if your TV doesn’t offer USB port), 3/ connect the OTG cable with the game pad.
3
First run : controller setup
The first run will extend the partition and automatically reboot.
Then, retropie will ask you to setup the controller.
Simply press each key and, when done, do a long press to ignore keys not present on your controller.