Yes, minors are allowed to invest in stock market in India. Parents or guardians operate minors' demat and trading accounts, thus, they can purchase shares on behalf of their minor kid. Minor's demat account only allows trading in the equity delivery segment. Minors cannot trade in intraday and futures & options segment.
In Zerodha, Parents or Guardians can purchase shares and gift them to a minor’s account. Minors cannot buy shares of any company but they can sell holdings from the demat account.