Question

can body have momentum with its energy negative

Answer 1

If energy of the body is negative then momentum of the body is imaginary.
$$\begin{gathered} E=\frac{P^2}{2m} \\ fornegativeenergy \\ -E=\frac{P^2}{2m} \\ P=\left(\sqrt{2mE}\right)i \\ somomentumisimaginary. \end{gathered}$$