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We reconsider the problem of the orbital dynamics of the innermost exoplanet of the υ -Andromedæsystem (i.e., υ -And b) into the framework of a Secular Quasi-Periodic Restricted Hamiltonian model. This means that we preassign the orbits of the planets that are expected to be the biggest ones in that extrasolar system (namely, υ -And c and υ -And d). The Fourier decompositions of their secular motions are injected in the equations describing the orbital dynamics of υ -And b under the gravitational effects exerted by those two exoplanets. By a computer-assisted procedure, we prove the existence of KAM tori corresponding to orbital motions that we consider to be very robust configurations, according to the analysis and the numerical explorations made in our previous article. The computer-assisted assisted proofs are successfully performed for two variants of the Secular Quasi-Periodic Restricted Hamiltonian model, which differs for what concerns the effects of the relativistic corrections on the orbital motion of υ -And b , depending on whether they are considered or not. • We study a quasi-periodic restricted model of the secular dynamics of υ -And b. • A Computer-Assisted Proof (=CAP) ensures there are exoplanetary orbits on KAM tori. • CAPs refer to two variants of the model, including relativistic corrections or not. • First ever CAPs for KAM tori in realistic models with degrees of freedom > = 3. [ABSTRACT FROM AUTHOR]