We present a sub-50-fs diode-pumped Kerr-lens mode-locked laser employing a novel "mixed" monoclinic Yb:Ca4(Gd,Y)O(BO3)3 (Yb:GdYCOB) crystal as a gain medium. Nearly Fourier-limited pulses as short as 43 fs at 1036.7 nm are generated with an average power of 84 mW corresponding to a pulse repetition rate of ∼70.8 MHz. A higher average power of 300 mW was achieved at the expense of the pulse duration (113 fs) corresponding to an optical-to-optical efficiency of 35.8% representing a record-high value for any Yb-doped borate crystal. Non-phase-matched self-frequency doubling is observed in the mode-locked regime with pronounced strong spectral fringes which originate from two delayed green replicas of the fundamental femtosecond pulses in the time domain.