0.3mm lead is the finest available on the European market. There is 0.2mm lead available on the Japanese market, but there are almost no pencils that use it. 0.3mm is mostly used for drafting purposes, but it's also used for writing where the user prefers a very fine line. However, the very fine width makes it inherently more prone to breaking than the larger diameters.
The widest range of lead grades available in 0.3mm is currently Uni's Nano Dia lead.
If your pencil specifies 0.35mm lead it should use 0.3mm lead OK. Faber-Castell 0.3mm lead specifies both 0.3mm and 0.35mm on the pack, and as far as we understand the two sizes are interchangeable.