Ginzburg-Landau theory for unconventional surface superconductivity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>PtBi</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math>

Recent experimental evidence suggests the presence of an unconventional, nodal surface-superconducting state in trigonal ${\mathrm{PtBi}}_{2}$. We construct a Ginzburg-Landau theory for the three superconducting order parameters, which correspond to the three irreducible representations of the point group ${C}_{3v}$. The irreducible representations ${A}_{1}$ and ${A}_{2}$ are the most likely. We develop a systematic method to determine the symmetry-allowed terms and apply it to derive all terms up to fourth order in the three order parameters. The Ginzburg-Landau functional also includes coupling to the magnetic field. The functional is employed to determine the effect of an applied uniform magnetic field on the nodal structure for ${A}_{1}$ and ${A}_{2}$ pairing. The results facilitate clear-cut experimental differentiation between these symmetries. We also predict field-induced helical superconductivity.