We study the higher derivative chiral models with four supercharges and Bogomol’nyi–Prasad–Sommerfield (BPS) states in these models. The off-shell Lagrangian generically includes higher powers of the auxiliary fields F, which causes distinct on-shell branches associated with the solutions to the auxiliary fields equation. We point out that the model admits a supersymmetric completion of arbitrary higher derivative bosonic models of a single complex scalar field, and an arbitrary scalar potential can be introduced even without superpotentials. As an example, we present a supersymmetric extension of the Faddeev–Skyrme model without four time derivatives, in contrast to the previously proposed supersymmetric Faddeev–Skyrme-like model containing four time derivatives. In general, higher derivative terms together with a superpotential result in deformed scalar potentials. We find that higher derivative corrections to 1/2 BPS domain walls and 1/2 BPS lumps are exactly canceled out, while the 1/4 BPS lumps (as compact baby Skyrmions) depend on a characteristic feature of the higher derivative models. We also find a new 1/4 BPS condition for domain wall junctions, which generically receives higher derivative corrections.