Access and modify files on the SD card of my mobile using WIFI tethering
You've got quite a few Apps that can do it:

Wifi File Explorer

Wifi File Transfer

3rd: WifiDroid, it doesn't let me post more than two links because of my reputation, but you can search in google.

4th: AirDroid, it allows you to transfer anything, and even control your phone with it.

I've used the first too, both free and pro versions, i like the 2nd more, the 3rd i never used.