If we want to make mannat for eg- if that person (family member) get shifa I will keep fast on four fridays, is this okay? Or we have to make niyyah of something else?

There are a few points:

– If one does not recite th sigha of nadhr as has come in the book of laws, then the nadhr is not wajib to follow on.

– According to Ayatullah Khamenei, if you have qadha fasts then you cannot make a nadhr/mannat for fasts. Instead you can make a nadhr that you will for example pay some of your qadha fasts together so will fast for 4 days together and pay back four qadha fasts.