Is the following problem NP-Complete? [closed]

3SAT with the additional condition that exactly 1 or 3 literals must evaluate to 1.

No. This problem is equivalent to XOR-3SAT, in which we interpret each clause as $$x \oplus y \oplus z$$, where $$\oplus$$ is the XOR operator, and ask whether it's possible to find values for all variables so that each clause is true. XOR-SAT can be solved in polynomial time using Gaussian elimination, with all arithmetic done modulo 2 (i.e., in the finite field $$GF(2)$$).