I presume you are on the rolls of a (Labour) Contractor who owns a license and has PF registration and is remitting the PF contribution in respect of other employees who are within the purview of PF. The Chief Engineer tried to avoid any violation in cutting and remitting the PF for everybody, and he is hesitant to grant you the exemption, so he is cautious. Although your salary is at 20K, you also mentioned it is CTC. Hence, it is not clear what is included in your CTC, perhaps the contribution towards your PF as well. In that case, it may be challenging for you to escape.
Of course, on your side, there is some reasoning as your appointment is a tenure post, and there is no likelihood of receiving a pension after completing one year. So your contribution to the Pension fund will be a loss to you only as you do not qualify for a pension. However, try to consider it differently. Suppose after this one-year tenure, you leave this contractor and secure a regular appointment with someone else (why not under the same chief engineer), there is a possibility of transferring your PF and Pension accounts to the future employer too. Try to think positively. I hope you are ambitious enough to aim for a bright future, my friend.
Regards,
Kumar.S.