Here is a list of the processors that your motherboard will support.
https://www.gigabyte.com/Motherboard/GA-F2A58M-HD2-rev-3x#support-cpu
Unfortunately an APU was a poor choice if you ever wanted to upgrade.
You buy a APU for the excellent integrated graphics.
But, there are no real good upgrades, particularly for a gamer.
If you install a superior discrete graphics card, you will have thrown away the big advantage of the APU.
Then, you are left with a relatively weak cpu. Most games depend on only a few fast cores.
Your A4-4020 is a dual core with a passmark rating of 1835 and a single thread rating of 1157.
One possible upgrade, for example might be a $140 A10-7850K with a passmark rating of 5500 and a single thread rating of 1571.
By comparison, a $65 kaby lake G4560 has a rating of 5108 and a single thread rating of 1993.
For other comparisons use google with the processor and passmark to find others.