On permutation trinomials of type $x^{2p^s+r}+x^{p^s+r}+\lambda x^r$

We determine all permutation trinomials of type $x^{2p^s+r}+x^{p^s+r}+\lambda x^r$overthefinitefield$$\mathbb{F}$_{p^t}$when$(2p^s+r)^4<p^t$. This partially extends a previous result by Bhattacharya and Sarkar in the case $p=2$, $r=1$.