Is there any sensor available to measure dc current from 0-100mA contactless?
Contactless is the problem, looked for some sensor half effect but they are for very high currents only
As I know there are only teoretical posibilities except Hall sensors. May be there are low-current Hall sensors?
For example, I have Unit UT210e clamp multimeter with 2 A DC current range and 1 mA resolution.
Measuring small DC currents via the magnetic field is difficult, as it is hard, as there are background fields. It can work reasonably if the wire goes through a closed core. Besides the hall effect sensors there are also flux gate type sensors, that can be more accurate, but are also more expensive.
As I know there are only teoretical posibilities except Hall sensors. May be there are low-current Hall sensors?
For example, I have Unit UT210e clamp multimeter with 2 A DC current range and 1 mA resolution.
I also have the UT210e - and it is a capable meter. The only challenge when measuring DC current is exactly this:
Measuring small DC currents via the magnetic field is difficult, as it is hard, as there are background fields.
For the UT210e this can be mitigated by keeping the meter as still as possible around the conductor and use the zeroing function until you get a stable (as can be) zero(ish) reading before turning the current on.
From my experience, accuracy (for non contact DC current) is not lab quality, but plenty good enough for the load measurements, resistor calculations, etc. you will encounter on the average work bench.
Even you have the exact probe you want, in order to get an accurate result at that level mA DC contactless-ly, the probing setup, the jig and the surrounding probing area will posed a challenge, as even a big metal object like a steel drawer nearby can affect the measurement.
Oh, the earth's magnet also will affect the probe too

, even after null-ing, you can't change the probe's orientation or sometimes even move around, or your probe will turn into sort of unwanted and annoying expensive compass.
The Tektronix TCPA , P6042 or plug-ins AM503. A, B, AM5030 will measure DC-100Mhz and down to 1mA. But all are expensive and require a scope to see results, at least for AC signals. I have a 503B that was part of a package deal and a 6042. Both work really well.
1. should be contactless, cannot disconnect wire or break it.
2. Accuracy is +-1mA or even 2mA can also work.
3. https://www.crmagnetics.com/Assets/ProductPDFs/CR5200%20Series.pdf have some solution for upto 2Amps.
Looking for some cheaper solution though,
Did you read the datasheet ?
Don't think the specified accuracy suitable for you, as even at 2A type, the "guaranteed" accuracy is only at 1%.
Meaning the error is around +/- 20mA, this is 10 times bigger error level than your requirement.
Its useless for you even you can afford it.
can you loop the current carrying conductor around a magnetic material? It boosts the magnetic strength by a factor of N. Moreover if you use a torroidal core of high Mu, you get even higher magnetic field which can be easily measured for 0 to 100mA range.
Here's an example of what multiple loops looks like:

5 loops giving a reading of 30.00A on the meter means the current flowing through the wire is 6.00A.
The loops do not have to look pretty for this to work. As long as the wire has enough length and is flexible enough, you can form these loops around one clamp arm with the jaws open - then let the jaws close and take your reading. The turns must all go in the same direction - you can't do a bifilar style wind as the net result will be zero, no matter how many turns you do.
Take the displayed reading and divide it by the number of times you count a section of wire passing through the inside of the jaws. In the above image, this number is 5.
Looks like this solves the purpose :
https://www.lem.com/en/ctsr-03p1. its contactless
2. can measure -300mA to +300mA with 1.9% accuracy.
can connect 16 bit adc and oversample it for better measurement.
do anyone else ever used their product, its reliablity?
You said you could not disconnect wire or break it ... that is a closed loop sensor.
You said you could not disconnect wire or break it ... that is a closed loop sensor.
Unless you are a true magician ...

Is there any sensor available to measure dc current from 0-100mA contactless?
Contactless is the problem, looked for some sensor half effect but they are for very high currents only
A DCCT ?
DCCTs were developed a long time ago at CERN to replace current shunts for high precision magnet current monitoring, now some commercial magnet power supplies use them too. These are
much more stable/precise (down to ppm range) than Hall sensors so that even with a relatively high current device you should be able to get a reasonable resolution. They aren't really cheap though (but I saw some reasonably priced on ebay).
I also found this project:
https://hackaday.io/project/329-dc-current-transformer