I and my client have agreed that we shall shift from hourly contract to fixed priced contract, but we want to make a fixed-price contract such that it recurs on weekly basis.
Is that possible on upwork?
You would have to create a new contract, as it's not possible to change an existing hourly one over to fixed price.
As for recurring, you could keep the same (fixed price) project open, and they could just add + fund a new milestone every time you needed it, perhaps?
He can add milestones. That's equivalent to hourly jobs, just I don't see what advantage does that have for you, except money is transferred earlier (under condition client doesn't take too long to approve milestone).