I dont think that you can treat different variables differently with a fixed effects model specification like yours. You will be demeaning all variables in $X_{it}$ and utilizing the withing individual variation. Also note however, that if you instead used a random effects model with following assumptions

1. $E(\varepsilon_{it} | X_{it}, \alpha_{i}) = 0$

2)$E(\alpha_{i} | X_{it})$ = 0,

then you will be using both within and between variation in your regressors (all the variables in $X_{it}$ however will be used).

Check Colin and Trivedi, Chapter 21 and 22  , Microeconometrics: Methods and Applications

I don't think that you can treat different variables differently with a fixed effects model specification like yours. You will be demeaning all variables in $X_{it}$ and utilizing the withing individual variation. Also note, however, that if you instead used a random effects model with following assumptions

1. $E(\varepsilon_{it} | X_{it}, \alpha_{i}) = 0$
2. $E(\alpha_{i} | X_{it})$ = 0,

then you will be using both within and between variation in your regressors (all the variables in $X_{it}$ however will be used).

Check Colin and Trivedi, Chapter 21 and 22, Microeconometrics: Methods and Applications.