I guess you're using a tuner. I don't have a dedicated tuner, I use a phone app called 'Sound Corset'. The center range on a note using the 'analog' gauge is + or - 10 cents. Depending on the reed and the state of warm-up the sax and I are in, I adjust the mouthpiece so all notes fit in that center range - some will be on the upper end, some on the lower end. This 20 cent center range is colored green so I don't have to peer at it or wear reading glasses during practice. I also use it on gigs, at least in the set-up/sound check period and having this app has made a tremendous difference in my effectiveness in general and working with other horns in particular. Now obviously you can't stare at a tuner the whole time and it can't react to short notes, but if you use it every time you pick up the sax it will show you some amazing things about playing in tune. Some of these revelations will not be pleasant but now is always the time to find out what you need to work on from the playing standpoint and/or the sax itself, which may need to be 'voiced' for individual note response and tuning. I was doing this with my tenor the other day on the notes with the adjustable bumpers on the guards. It is also sometimes surprising how much reed selection can change intonation. This is because cane reeds can be different in resistance - when you have to play with more pressure, you'll find you also have to compensate for tuning with your embouchure. If you could find a synthetic you like, you can at least take that out of the picture because as long as it lasts, it will be pretty much the same every time.
Sometimes you have to get a better mouthpiece or horn if you can't manage intonation, but you probably should get with a good teacher before getting on the mouthpiece train. OTOH, if you're using a Chinese sax and trying to play the stock mouthpiece, picking up a name brand mouthpiece in about a #5 to #7 facing could be a big boost for you.