If someone intentionally broke fast knowing its wajab but was not aware of any rulings regarding of the breaking of the fast and only was thinking whatever they miss they can just make it up later or something along those lines what should they do in thos case. Should they make up just those days they missed (10 days) or do they have make up 60 days for each they missed.

And what would be the kaffara due in such a case if any?

If you were aware that breaking the fast is haram, then you pay the kaffara, which is either feeding 60 needy persons for each day, by handing 750 gms of rice or flour to each one of them, or fasting 60 days for each broken day. Hence you need to fast 10 days, and feed 600 poor people (if you chose to feed needy people)