How much time should my child spend on studying chess?

It depends, on what your child's goal is for his/her chess development.

According to the 10,000-hour rule, here is a rough guideline:

• if s/he wants to be a GM or IM, 6 hours everyday, expecting 6-10 years
• if s/he wants to be nationally ranked, national champion or a NM, 2-3 hours everyday
• if s/he wants to be state champion, 1-2 hours everyday
• if s/he wants to play competently in local tournaments or keep making progress, 1 hour everyday
• if s/he wants to enjoy chess, any as long as s/he is having fun

Alice: Would you tell me, please, which way I ought to go from here?
The Cheshire Cat: That depends a good deal on where you want to get to.
Alice: I don't much care where.
The Cheshire Cat: Then it doesn't much matter which way you go.
Alice: ...So long as I get somewhere.
The Cheshire Cat: Oh, you're sure to do that, if only you walk long enough.
― Lewis Carroll, Alice in Wonderland