Step back a bit. The filter (which is in the tank on an MPI) is very unlikely to be blocked so much that it affects the fuel flow. Modern benzina doesn't have all the bits that came free with every gallon of 2-star back in the day (kids, ask your dads).
Also, Seicento normally/as standard has Multipoint Fuel Injection, not a carburrettor, so if you have a carb' fitted then that's probably the problem right there.
If it fails to pick up revs using the throttle but goes well with a squirt of the magic fairy juice, then it's either electric or fuel that's the problem.
Check that all four cylinders produce a spark. Connect the HT lead of one cylinder at a time to an old plug laid on the engine (don't hold it there unless you're very well insulated) and run the engine or turn it over to see whether or not there is a spark.
If there's a duff coil, you'll find that two of the plugs don't fire and the other two do (I think they're paired 1&4, 2&3). New coil is a simple swap and not too dear.
If the sparks looks okay, then the problem could be a duff injector (if you have MP's in your I). Remove the connector block from each injector in turn and stuff a multimeter against the terminals .. then crank the engine over and see if you get any volts. You can use those glass bottomed bulbs with the wire tangs for this... just unbend the wire tangs and hey presto, they exactly fit into the injector plugs.
If you have sparks and injector juice, you need to take out the injectors and see whether they all work properly. I would do the "spark plug" test.. remove each plug and see whether one of the plugs looks cleaner or dirtier than the others. If an injector is lazy, I would expect the plugs to be cleaner (leaner) in that cylinder.
If you can get hold of a spare good injector for not much money, then swapping out the most suspect one would be the DIY method of solving it.. a garage might have a flow tester to test the injectors and make it less of a hit and miss and pray job... (but would require money).
If it runs well enough to run it around.. put some injector cleaned in the tank. RedX or something like that... use the maximum suggested dose and run the engine around for half an hour to get it properly hot.. and use some revs to vary the fuel flow. You don't need to cane the beast to an inch of it's life... just give it a workout.
If the sparks, injection and injectors all sound good then you may have duff fuel pressure... the regulator might be weedy but there's no easy way to test this (you need a fuel pressure gauge, which matey mechanic will have but for a fee).
You can test there's fuel in the fuel rail by disconnecting the fuel line to the injector rail and cranking the (cold) engine over. Catch the fuel in a small jar and don't smoke any ciggies while you're doing it. If you get a gush of fuel then the regulator and the pump (including filter) are fine. If it's a weedy dribble... then one or the other or both could have failed.
Don't rule out the pump, if there's no good fuel flow.. sometimes it "works" but may be spinning but not actually delivering, if the pump vanes are detached... or the lifting pipe/if it's rubber could be split.. etc.
You won't get any error codes if the pump/regulator have a problem since they're mechanical. Injectors, coils and plugs might, since they will be giving a duff resistance to the ECU... but the Cinq'/Sei is old and the systems were not so flashy back then (early Cinq's came with a ride-on mechanic) so the car OBD might not be as clever as systems are now.
Ralf S.