Tecnam P2012 Traveller Captain reported autopilot failure while descending to land.

Narrative

CA is PF; FO is PM. We were coming back from ZZZ1. Normal flight; cold and icy. We were given block 8-10 from ZZZ CTR (Center) (I told my FO to ask for it before) and was navigating through the block to be above the clouds and looking for best tailwind. We got handed off to ZZZ APP (Approach) around 56NM from the field. Around 45NM we were in IMC and light rime at 9;000ft. Altitude above was not good and altitude lower was gonna get us better tailwind so we did a slow descent to 8;000. At this point we were in IMC and in light rime and we knew we won't see the ground until at least minimums on approach. Again; everything is indicating normal. I was heads down on my EFB and all of a sudden my FO said 'airspeed disagree!'. I looked up and saw the indication and I mentioned that we have seen this before; nothing to worry about; pull the QRH and run it. Shortly after that thr AP (Autopilot) disconnected on its own accompanied with the red AFCS flag; so I had to take control and manually hand-fly the aircraft. We ran the QRH and ADC 2 was a good one so I selected it on my PFD (Primary Flight Display) and I got my AP back so I engaged it. Then we looked further into the QRH for more information and guidance but nothing more than what we were just doing. Shortly after; the AP disconnecteded on its own again. At that point we re-did the QRH action items and I decided to reset the autopilot master to see if there is a reaction but it did nothing as the red flag was still up. At this point my speed tape is dropping slowly and I was checking to see if ADC 1 is getting any better or not but it's showing around 30kts slower and around 200ft lower than ADC 2; so we decided that I'm flying on ADC 2. We were also constantly confirming with ZZZ APP on our altitude and what they were showing and it was a part of the decision making to use ADC 2. Shortly after that; my speedtape is starting to roll back. I looked outside and yes we are in icing but the TKS system is doing its job so I know we're not getting iced up. I looked at ADC 1 just to compare and the IAS is at 40 kts and slowing. I switched back to ADC 2 and I told my FO to tell ZZZ APP to request priority handling and keep us on a tight vector/approach. My FO did a good job keeping company in the loop over the radio. As we were getting vectored; my speedtape eventually made it to 0 and the red X pops up. My standby AI and IAS is also gone (red X). FD (Flight Director) was also not doing what I was commanding it to do (via FO since I'm hand flying) so I told my FO to kill it and fly raw data instead. At this point I have no idea how fast I'm going; GS was inaccurate; and winds aloft indication was showing 100kts tailwind at some point (inaccurate). I'm going based off of my power settings and experience to feel how fast we're going and got the TKS on MAX. We decided to fly a bit faster so we don't risk anything for no reason so I got established as best as I can and kept a faster approach and executed a no-flap landing to prevent risk of using the flaps and overspeeding it. Back taxi on the runway since aircraft was blocking Taxiway 1 and taxi slow to the ramp accompanied by 2 fire trucks. Shut down; said goodbye to the 2 pax (Passengers) like normal (they had no idea what was happening which was intentional); and I told my FO to help me with the can as I immediately jumped out to inspect my static ports; pitot tubes; and drained the static line per the QRH. Everything was clear; no ice; no liquids; no blockages. Pitot tubes were hot and I can hear snowflakes hissing as it touches the tubes and melts it to vapor. Nothing came out from the static line drain plugs.