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Recent nuclear magnetic resonance and calorimetric experiments have observed that UTe₂ exhibits a transition between two distinct superconducting phases as a function of magnetic field strength for a field applied along the crystalline b axis. To determine the nature of these phases, we employ a microscopic two-band minimal Hamiltonian with the essential crystal symmetries and structural details. We also adopt anisotropic ferromagnetic exchange terms. We study the resulting pairing symmetries and properties of these low- and high-field phases in mean-field theory.