The way to approach this sort of thing (when you get an unexpected result) is to try to divide the problem to see where your assumptions went awry.
The sensor is guaranteed (from the factory, assuming it's not damaged) to be within +/-1% at 25°C and the \$\beta\$ is 3950 +/-1%.
Let's see what that means at 25°C - using an online calculator out of laziness, that's about +/-0.23°C. 4°C should be 27287.5K according to the \$\beta\$ model, so a 1% error in \$\beta\$ contributes about another 0.2°C. So we would expect the error due to the sensor to be less than 0.5°C worst-case and perhaps a fraction of that typically. This is something you can check with a multimeter if you have confidence you actually know the temperatures that closely. Even if your multimeter is only good to 0.25% accuracy, the repeatability is much closer.
This would be a good first check to see if the problem is your circuit or your sensors and/or their application and mounting or even real temperature variations.
As far as the op-amp circuit goes, you have an error of +/-3.5mV. That represents a potential resistance error of about 0.3% or less than 0.1°C at 25°C and perhaps 0.2°C at 4°C. Assuming a 5V supply, worse with a 3.3V supply.
ADC error is several times that worst-case, at 4°C
There are a few other errors such as self-heating.
So worst-case we could see unadjusted errors in that range, but it seems unlikely to get worst-case error that large.
Let's consider self-heating- 3.5mW/K is typical of an 0805 mounted on a PCB.
Power dissipation is worst-case at 25°- with a 5V supply you have 2.5mW which would account for almost 1°C error depending on whether your PCB and how much copper it has etc. If the part was floating in air with thin leads it might be considerably worse.
It's a bit strange that you added resistance to the series resistor to make them read 'correctly' since one would expect them to require a lower resistance due to self heating. Perhaps you also fiddled the equation? If that was done improperly (for example, by subtracting a constant from the ADC reading) that could add enormously to the error at temperatures far from 25°C.
If you still think your circuit/equations might be the problem, replace the sensors with precision resistors of 10.00K/27.288K (or whatever your tables say the resistances should be) and compare the readings.
Reading accurate to a fraction of 1°C is actually not so easy. Getting a reading with a high resolution is dead easy with at thermistor or an RTD or a semiconductor sensor, but that's only part of the problem. Things like self-heating and thermal conductivity of wires can add significant errors. You can look at how calibration of probes is checked at standards labs.
And, of course, it's always possible the sensors themselves are not as accurate as claimed.