In panel regressions you have multiple dimensions and that is why also you have 3 different $R^2$. The within $R^2$ tells you how much variation within your panel variables is on average explained by your model. The between $R^2$, tells you how much variation between your panel variables is explained by the model, and overall $R^2$ gives you the combination of both and tells you how much variation in the whole panel data your model explains.
According to the stata manual you should get adjusted $R^2$ for fixed effects by
ereturn list it will be the r2_a scalar. However, there are no simple adjustments for within and between $R^2$, those are most often reported unadjusted.