Those 3.5 HP Briggs & Strattons have been around forever and I can think of at least 3 places that fuel filters have been located. Check at fuel tank outlet or carb inlet. Sometimes this has just been a piece of brass screen wire. At other times, they have used a small in-line pleated paper filter. Sorry that I can't be more help. I suggest that you start by removing the carb fuel bowl and check around there. The condition that you describe could also be caused by a gunked up or mis-adjusted needle valve. Be careful when working with the bowl off as parts can tend to fly as you remove it and the spring that holds the needle in place tends to wander off easily, same for the float pivot bar.