You can file a writ petition before High court Madras, through an advocate who practices in Madras High court invoking article 226 of the Indian constitution;
The relevant rules under which you can seek the relief against the passport officer to issue the passport to your Indian citizen minor child is given below:
1[3. Citizenship by birth.—
(1) Except as provided in sub-section (2), every person born in India,—
(a) on or after the 26th day of January, 1950, but before the 1st day of July, 1987;
(b) on or after the 1st day of July, 1987, but before the commencement of the Citizenship (Amendment) Act, 2003 and either of whose parents is a citizen of India at the time of his birth;
(c) on or after the commencement of the Citizenship (Amendment) Act, 2003, where—
(i) both of his parents are citizens of India; or
(ii) one of whose parents is a citizen of India and the other is not an illegal migrant at the time of his birth, shall be a citizen of India by birth.