Assalamu Alaykum wa Rahmatu Allahi wa Barakatuh

If the clinic is exclusively for the poor and needy, it is permissible to use Zakah for building it because having a clinic is a necessary vehicle for providing health service including medicines. I say that knowing that there is another opinion that does not allow it. Here we need to expand the argument a little. Services, health, education , transportation, etc. are part of contemporary life. Services are considered properties in our Shari’ah. So you can buy them and sell them and finance them through Islamic banking and finance. Why not give them on the basis of making the poor own them also as he/she owns physical things when you give him food or cloth.

Wa Allahu A’alam

Wa Alhamdu Lillahi Rab al Alamin