Examples for Partial Combinatory Algebras
Consider a subPCA $A$ of Kleene's first algebra. It contains $K$ and $S$. These are sufficient to implement every total computable function, so $A$ must contain at least these, and cannot be just some limited complexity class.

I do not quite understand why Kleene's second algebra and Scott's graph model aren't "topological". Kleene's second algebra is the universal 0-dimensional countably based Hausdorff space. Scott's graph model is the universal $T_0$ countably based space. These characterizations have no trace of computability, but because the spaces are universal it is to be expected that they have a very rich structure, and so can be made into models of $\lambda$-calculus.