The magnetic and superconducting properties of a series of underdoped (BNFA) single crystals with have been investigated with the complementary muon-spin-rotation () and infrared spectroscopy techniques. The focus has been on the different antiferromagnetic states in the underdoped regime and their competition with superconductivity, especially for the ones with a tetragonal crystal structure and a so-called double-Q magnetic order. Besides the collinear state with a spatially inhomogeneous spin-charge-density wave (i-SCDW) order at and 0.26, that was previously identified in BNFA, we obtained evidence for an orthomagnetic state with a “hedgehog”-type spin vortex crystal (SVC) structure at and 0.34. Whereas in the former i-SCDW state the infrared spectra show no sign of a superconducting response down to the lowest measured temperature of about 10 K, in the SVC state there is a strong superconducting response similar to the one at optimum doping. The magnetic order is strongly suppressed here in the superconducting state and at there is even a partial reentrance into a paramagnetic state at .