Can children claim maintenance?

Yes. Both Section 20 of HAMA (Hindu Adoptions and Maintenance Act) and Section 144 of BNSS (Bhartiya Nagarik Suraksha Sanhita) make it a parent's duty to maintain their children and this includes illegitimate children too, not just those born within marriage. The general rule is that this obligation lasts until the child turns major. But if the child even as an adult, is unable to support themselves because of a physical or mental disability, the obligation can continue beyond that.