Momentum of a particle of mass $m$ is $p$. Its kinetic energy will be

Kinetic energy ($KE$) and linear momentum ($p$) are defined as:
$$KE=\frac{1}{2}m{v}^2,p=mv⟹v=\frac{p}{m}$$
Substitute $v$ into the kinetic energy formula:
$$KE=\frac{1}{2}m{\left(\frac{p}{m}\right)}^2=\frac{1}{2}m\frac{p^2}{m^2}=\frac{p^2}{2m}$$