Malta-Istanbul-Beijing 144 hour transit free visa

Hi, good evening
We have a flight from Malta to BJ via Istanbul (Turkish Airlines) we have 3 hours connection flight and we do not go out from the airport. We are going to stay 3 nights in BJ before we take Royal Carribean cruise from Tiajin to Singapore. Then flight from Singapore to Malta. Can we apply for the 144 hour transit visa, or better If we apply from Malta? How long does it take to get it in the airport?
Our nationalities are Maltese, and Hungarian.
Thank you in advance.
Jonathan