If a Telugu speaking woman married an English man and the children speak the two languages equally well and that is possible in the global context.
What will be the mother-tongue of the children.?
Is there a word like father-tongue?
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A distinction is sometimes made by some speakers (who are not usually fluent English speakers), who treat "mother tongue" compositionally rather than as a technical term meaning (well, that in itself is a problem) "native language" or "first language", often labeled "mother tongue". For example, "My mother tongue is Pare and my father tongue is Gogo". Linguists usually approach the problem more conversationally by asking a person about the languages that they speak, and which ones they use for what purpose. In that context, if you were to have started by asking "What is your mother tongue?", you could get an answer to the question "which of your two 'dominant' languages does your mother speak?", and you might need to probe deeper to find out about their "father tongue".
Native English speaking linguists generally do not talk of languages being "tongues", so as a technical term, "father tongue" is unusual. You may encounter it in non-technical contexts as in the Gogo / Pare example, or as a somewhat quirky term for a language revitalization effort (read about the project name here). There is, though, a journal called Mother Tongue, which is about language prehistory, and this inspired the construction Father Tongue hypothesis, which has nothing to do with what languages you or your parents speak.
I don't know if speakers of Indian English would find it unusual for a person to say "My mother tongue is Telugu and my father tongue is English".
The idea of mother tongue can break down when you have more than one language learned by the child. Multilingual families are often the ones who see this the most.
There are various labels for all the different functions of each language, e.g. "dominant language", "first language", but I think "mother tongue" and "native language" are the only ones that are common enough to be recognised by most English-speaking people.
One specific use of the term "father tongue" was coined to explain how the Y-chromosome (only passed from fathers to sons) links to language acquisition, and one proposed reconciliation of mother tongue vs father tongue is the hypothesis that children learn phonemes from the mother but lexicon from the father.