In 1973, Casselman established the theory of local newforms of $\mathrm{GL}_2$,
which bridges a gap between elliptic modular forms and automorphic representations of $\mathrm{GL}_2$ over the rational fields.
In this talk, we introduce compact open subgroups of quasi-split even unitary groups over $p$-adic field for each even non-negative integers,
and explain the theory of local newforms for irreducible tempered generic representations with a certain condition on the central characters.
To do this, we introduce the Fourier-Jacobi modules of irreducible representations.