I am in US on L1 VISA and will go back to my home country before I complete 183 days here in US there by having non resident status.
I want to apply for SSN here so that I could get phone connection and credit cards etc, I want to know that if I get SSN would I be required to file my tax here in US as well which is not required at all if I do not have SSN.
Any help/suggestion is appreciated, *** guide me

If you are not required to file tax in U.S. this fact does not change if you have SSN.
However, you must make sure if you are required to pay tax or not. Normally, L1 visa holders from India pay tax even the stay is less than 183 days unless the salary/wages is not paid by any establishment in the U.S.

There are TWO considerations as to whether you have to pay taxes on income earned in the U.S.

The first you are aware of, that being the 183-day Substantial Presence Test.

The second is whether the salary is U.S.-sourced. If you are being paid by a U.S. company or a U.S. subsidiary of a foreign company, then the income is taxable whether you are here ONE day or 182 days.