Multimode quantum light fields significantly enhance quantum state manipulation and communication capabilities by expanding the dimensionality of the Hilbert space. In this work, we elaborately design a non-horizontal cavity suitable for a Gouy phase-compensated synchronously pumped optical parametric oscillator. By injecting an optical frequency comb in HG10 mode into the cavity as the seed, we demonstrate the simultaneous generation of a bright squeezed optical frequency comb in HG10 mode and a vacuum squeezed optical frequency comb in HG01 mode. The coexistence of amplitude quadrature squeezed fields in these two orthogonal first-order Hermite-Gaussian transverse modes also suggest the presence of quadrature entanglement between the two first-order Laguerre-Gaussian modes, LG0 + 1 and LG0 - 1. This research underscores the capability of one-step generation of multi-transverse-mode squeezed optical frequency combs using a single cavity, marking a significant stride in the realm of quantum optics.