Is there a jump process that in any finite interval, there can only be maximally one jump?

Question

If the jump process has a jump rate $\lambda$, is there a process such that $$\mathbb{P}\left(N(t+h)=n+m|\hbox{ }N(t) =n\right) =\begin{cases} 1 - \lambda h + o(h) & \text{if }m=0\\ \lambda h + o(h) &\text{if } m=1,\\ 0 & \text{if } m>1,\\ \end{cases} $$, where right here, $m>1$ is not $o(h)$, but 0? So extending to any large interval, $m>1$ scenario cannot occur, i.e. no two or more jumps.