We investigate the galaxy quenching process at intermediate redshift using a sample of $sim4400$ galaxies with $M_{ast} > 10^{9}M_{odot}$ between redshift 0.5 and 1.0 in all five CANDELS fields. We divide this sample, using the integrated specific star formation rate (sSFR), into four sub-groups: star-forming galaxies (SFGs) above and below the ridge of the star-forming main sequence (SFMS), transition galaxies and quiescent galaxies. We study their $UVI$ ($U-V$ versus $V-I$) color gradients to infer their sSFR gradients out to twice effective radii. We show that on average both star-forming and transition galaxies at all masses are not fully quenched at any radii, whereas quiescent galaxies are fully quenched at all radii. We find that at low masses ($M_{ast} = 10^{9}-10^{10}M_{odot}$) SFGs both above and below the SFMS ridge generally have flat sSFR profiles, whereas the transition galaxies at the same masses generally have sSFRs that are more suppressed in their outskirts. In contrast, at high masses ($M_{ast} > 10^{10.5}M_{odot}$), SFGs above and below the SFMS ridge and transition galaxies generally have varying degrees of more centrally-suppressed sSFRs relative to their outskirts. These findings indicate that at $zsim~0.5-1.0$ the main galaxy quenching mode depends on its already formed stellar mass, exhibiting a transition from the outside-in at $M_{ast} leq 10^{10}M_{odot}$ to the inside-out at $M_{ast} > 10^{10.5}M_{odot}$. In other words, our findings support that internal processes dominate the quenching of massive galaxies, whereas external processes dominate the quenching of low-mass galaxies.
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