council housing
To be entitled to a municipal apartment, you must be an Austrian citizen or have equivalent status, i.e. you must be a permanent resident of the EU, an EU/EEA citizen with a permanent registration certificate or an asylum seeker. If you have had your main residence at the same address in Vienna for two years, the chances of you being able to apply for a so-called residential ticket increase.
You can find more information about municipal housing here: https://wohnberatung-wien.at/wiener-wohn-ticket/allgemeines
cooperative apartment
Cooperative apartments (or subsidized apartments) are usually significantly cheaper than apartments on the free market. However, a type of deposit (financing contribution) must be made, which can be quite high. This is refunded at the end of the tenancy, minus a small sum.
You can find cooperative apartments through private advertisements, at the respective non-profit housing associations or through the Vienna Housing Advice Center ..