paternal cousin, on the (my) father's side These would all be less awkward English translations or at least acceptable.
"He is a cousin from the father side" is not English. Correct versions: "He is a paternal cousin"; "He is a cousin on the father's side." Also accept "He is a cousin from the father's side" (though not technically correct, it is sometimes heard).
'The father's side'' IS (the) correct English; ''the father side'' - which is the given translation - is incorrect.
I agree with all the other people in this discussion. In English, the correct translation would be "He is a cousin on his father's side"