The biggest patrons of Beethoven were Archduke Rudolph, Count Andreas Razumovsky, Prince Kinsky, and Prince Lobkowitz. Archduke Rudolph was Emperor Leopold's youngest son, and he is considered the most important of all the patrons of Beethoven.
Beethoven did make 14 compositions and dedicated them to him after Rudolph started to study with him in the year 1804. This includes "Archduke trio" (piano trio in B-flat major Op. 97), and the Missa Solemnis. Rudolph also did a composition which he dedicated to Beethoven. Another patron of Beethoven, Andreas Razumovsky, commissioned Op. 59, Nos. 1-3 (Razumovsky Quartets).
Only three of these patrons agreed to play Beethoven, and it was only Archduke Rudolph that ended up paying. Prince Kinsky did die when he fell from his horse, while prince Lobkowitz refused to pay again in September 1811. He expected Beethoven to publish his compositions and get his small pension remaining to meet his needs.