How to apply a operator to qubit system on the basis of current state of system?

I assume that you have a qubit register $q$ and given that the state of $q$ is $|psi_irangle$ you want to apply $U_i$ to $q$ for $i=0,1,2$. If this is what you wish to do, then unfortunately if the states $|psi_irangle$'s are not orthogonal to each other, then this kind of operations are not possible in a quantum setting in for any general $U_i$'s. This is not possible because such an operator is not unitary. For instance take the simple case of $q$ being in either the state $|0rangle$ or $|+rangle = frac{|0rangle + |1rangle}{sqrt{2}}$ and I wish to apply $I$ on $q$ if it is in the state $|0rangle$ and $H$ gate on $q$ if the state of $q$ is $|+rangle$. This mathematically would mean that I need an operator $U$ that works as follows: $$U|0rangle=|0rangle text{ and } U|+rangle = frac{1}{sqrt{2}}(U|0rangle + U|1rangle) =|0rangle.$$ It is quite obvious that $U$ is not reversible and hence is not a unitary. So such a quantum operation does not exist.

However, if the states $|psi_irangle$'s are orthogonal to each other and the state in $q$ is one of these states and is not any superposition of these states, then certainly you can measure and then conditioned on the measured result you can apply the $U_i$ of your choice.