> I was trying to play some Mod files that I moved from a previous OS4.1 system that
> I owed before, in AmiNet Radio Player, but all I get is high pitched short bursts of noise.
> Is this a compatibility issue?

No, this is most likely an issue of disabled ANR MOD player. Go to "Settings" -> "Settings" -> "Players", select "ptplay.player", tick "Activate" and click "Save".
There're also other MOD-compatible players for ANR:

http://aminet.net/package/mus/play/ANR_modplayer
http://aminet.net/package/mus/play/anr-modplug

> Or is there any other way to play those files?

Yes, UADE and Delitracker come to mind.

> Are there any other sources to download MOds compatible with Morphos players?

Other sources than what? Your question sounds somewhat weird as basically any MOD file in existence should play with any of the above-mentioned programs and ANR players.