Super Yangians in characteristic $2$

We define the super Yangian $Y_{m\mathrm{\mid }n}$ over a field $\text{mathbbm}k$ of characteristic $2$, and show that the super Yangian $Y_{m\mathrm{\mid }n}$ is a deformation of the super universal enveloping algebra of the current Lie algebra ${\mathfrak{g}\mathfrak{l}}_{m+n}[t]$. By employing the methods of the work of \cite{BT18}, we also give a description of the center of $Y_{m\mathrm{\mid }n}$.