thats not an issue .the difficulty level is different but u will have the same basic subject for these exams.

the depth differs so solve difficult questions which would be useful for both and also the time management.

No you don't need to study separately. If you are preparing for jee then syllabus of kvpy is also covered.Study hard and cover all basics .Basics are really important. Giving a mock test of KVPY is also very beneficial as it gives an idea on the preparation level from time to time. Best of luck.