Is it possible to pursue BA in one year after completing 3-year polytechnic diploma?

Yes, you can apply for B.A. (second year). In this case, the 3-year Polytechnic Diploma would be considered as an alternative for an intermediate course.

You cannot take lateral admission in the 3rd year of BA as per the guidelines of UGC, but you can apply for engineering program in the 2nd year through lateral entry. First, you need to decide the best career option for yourself because your choice will decide the future of your higher education.