We investigate frequency doubling of focused Bessel-like higher order fiber modes in a one-dimensionally quasi-phase matched structured KTP crystal. A single higher-order fiber mode, LP0,7, was generated at 971 nm using a fiber optical parametric amplifier pumped by sub-nanosecond pulses at 1064 nm. Frequency doubling to 485.5 nm was achieved with a maximum conversion efficiency of 48%, which produced a highly structured blue beam without any brightness improvement with respect to the fundamental beam. By optimizing the phase mismatch, we also experimentally demonstrate clean on-axis conversion-resulting from cascaded chi((2)) : chi((2)) processes, which is in good agreement with our numerical simulations, that give rise to brightness enhancement.