The query is too sketchy. As suggested by learned expert, Mr. Hemant Agarwal has suggested the issue could be understood in the context of the surname of the child of the inter-caste marriage or in the context of eligibility for benefits extended by the Government.
In respect of surname, it is a matter of choice: the child even has option to have no surname at all, or even a surname other than that of the father and mother (if at all they have surname).
As regards to benefit of reservation etc. the child, generally, takes up the caste of the father. But the situation could be different if the child was brought up in the mother's community. The principle in this context has been laid down by the Supreme Court in the case of Rameshbhai Dabhai Naika v. State of Gujarat:
"43. In view of the analysis of the earlier decisions and the discussion made above, the legal position that seems to emerge is that in an inter-caste marriage or a marriage between a tribal and a non-tribal the determination of the caste of the offspring is essentially a question of fact to be decided on the basis of the facts adduced in each case. The determination of caste of a person born of an inter-caste marriage or a marriage between a tribal and a non-tribal cannot be determined in complete disregard of attending facts of the case. In an inter- caste marriage or a marriage between a tribal and a non-tribal there may be a presumption that the child has the caste of the father. This presumption may be stronger in the case where in the inter-caste marriage or a marriage between a tribal and a non-tribal the husband belongs to a forward caste. But by no means the presumption is conclusive or irrebuttable and it is open to the child of such marriage to lead evidence to show that he/she was brought up by the mother who belonged to the scheduled caste/scheduled tribe. By virtue of being the son of a forward caste father he did not have any advantageous start in life but on the contrary suffered the deprivations, indignities, humilities and handicaps like any other member of the community to which his/her mother belonged. Additionally, that he was always treated a member of the community to which her mother belonged not only by that community but by people outside the community as well."