If the concerned school is refusing to accept the TC provided by the previous school, then you can report the matter to the District collector with a complaint against the school as well as the DEO who is refusing to counter sign the TC, keeping the child's education at stake.
Section 5 provides children the right to seek transfer from a Government or Government aided school to another such school in order to complete elementary Page 3 education and for immediate issue of Transfer Certificate to a child seeking admission to another school.
Right to education explained in law:
freedom of parents to choose schools for their children which are in conformity with their religious and moral convictions. freedom of individuals and bodies to establish and direct education institutions in conformity with minimum standards established by the state. academic freedom of teachers and students.
While the above being the fact, just for their own ego and for any other reason, one authority after another cannot drive the student or the parents from pillar to post denying their rights.
If you do not get any relief or remedy from District collector too, then you may file a writ petition before high court seek relief on this with appropriate directions to the concerned authorities and the new school to admit the child