Non-complex cobordisms between quasipositive knots

We show that for every genus $g\ge 0$, there exist quasipositive knots $K_0^g$ and $K_1^g$ such that there is a cobordism of genus $g=\mathrm{\mid }{g}_4(K_1^g)-g_4(K_0^g)\mathrm{\mid }$ between $K_0^g$ and $K_1^g$, but there is no ribbon cobordism of genus $g$ in either direction and thus no complex cobordism between these two knots. This gives a negative answer to a question posed by Feller in 2016.