I am an aspirant of Gate 2021 CE. But, want to give the paper of 2020. My 3 subjects are very strong (given topicwise & subjectwise tests on it) but am average in the other 3 subjects. Should I first complete the Topicwise & Subjectwise first of those 3 subjects or directly jump in the Full Paper?

I think you should attempt the 2020 GATE entrance. So you can get the of where you stand in the all over India.
As per guidelines, there is no attempt limit or limit barrier.you can evaluate yourself by giving an upcoming exam.
You have 2 months in your pocket try to study high marks subject from the remaining 3. Revise the 1st 3 subjets and Do solve the MCQ and give a mock test before exam.
Best luck.