I have a 1987 samurai that turns over,has good compression has been timed properily has fire to plugs gas to the carb but will not start

the G13 or G16 engine, and 1987 year was carbs, not EFI.
so if it has carb , you need to say so.

if it starts fast with test fuel (spray)
then your choke is dead.
ever adjust a choke before.
RTM?

https://suzukipitstopplus.com/Products/10163-1986-1987-samurai-service-manual.aspx

still stock with stock carb? or it EFI.?
some are. newer.
no matter all gas motors same.
1: compression bad, (timing belt to cam bad)
2: no spark (or timed wrong ) you did only 1 of 2 tests.
3: bad fueling. try test fuel
1,,2 3, in that order or go crazy chasing tail. .

carbs are tuned for you altitude. (what country?)
is car still stock, many are not. not this old.
and to tune it takes a 5 Gas Analyser or AFR meter.
once tuned , the Cat converter cleans up the retainer,
the full manual is here, for USA.
http://www.acksfaq.com/sitemap.htm

To avoid the running out of fuel in the carb,one simple suggestion. Fit a Check valve ( metallic one ) between the fuel pump and carburetor.Always the non return to be on the side of the carburetor.

Hmmm, love those old Festiva's, great cars. Sounds like you may have a worn bushing in the distributor causing the timing to change under load. Remove the distributor cap and see if you can move the shaft side to side any. If that's good, check your spark plug wires by inserting some known good plugs into the wires , ground the side of the plugs to the engine while someone else turns the engine over. If each plug is firing a nice blue spark hot spark then your plug wires are good. If you haven't changed the spark plugs do so, even new ones can be bad. Next is fuel, old carbs are problems esp if the car has sat a while. Weber 2 stage for about $220 is a sure cure for a bad carb, I have one on my Samurai 1.3.
You didn't say if the car has ample power when it's running ok. Do a compression check to see if your valves need work. All gas engines must have compression, fuel, correct timing on firing the sparkplugs. Last but not least if all else is good use a timing light to see if the timing is advancing when you rev the engine.

I had a similar issue with my '86....driving home, made a left turn, and engine shut down. Coasted to a stop, and had a look under the hood. Cranked over fine, had gas, spark, but no go! After a tow home, and more in-depth investigating, turned out that the timing belt had broken! The older engine has no interference between valves and pistons, so installing a new belt got 'er going again for about $40. You can look down though the oil fill port or loosen the upper screws on the belt cover to confirm that the valves are/are not moving when the engine cranks.
mr_haney2u

Any time a car sits for a long period of time you should completely drain the gas tank. The gas is more then likely stale. Try pouring a little new gas into the carb or use starting fluid. If it starts you have found your problem and will more then likely have to drain and clean the tank and replace the fuel filter.
If it does not start with the new gas, it is either a compression or timing issue. If you have spark at the plugs, and GOOD fuel in the carb and it still wont start I would check the timing. If the timing is on, check compression. If the engine sat to long with no oil in the cylinders they can build up condensation and rust. Then when you try to start it with the rust in the cylinders it can destroy the rings and cause compression loss.

if the timing is off you wouldn't have good compression
make sure you have at least 136-170 psi and the different should not be more than 14 psi.

The best information I have is;
The order is 1-3-4-2
This is the Firing order for the 1987 suzuki samurai with a 1.3 motor.

When changing plugs, do them one at a time to prevent mixups.
When changing plug wires, do them one at a time to prevent mixups.

It sounds more like a timing problem. If it backfires through the carb that means the intake valve is open when the spark plug fires. Same with the exaust but it the exhaust valve that is open.