Overstayed in China for 13 days

I seriously doubt that any of forum active respondents will and can answer your question. The problem you have described is simply too complex for this section and I seriously think that only relevant person is the one from the Chinese competent institutions.

Based on numerous data points, the immigration blacklist simply pertains to visa issuance, which is the responsibility of the embassy or consulate, and NOT to residence permit issuance which is under the jurisdiction of the Exit and Entry Administration. Further details are needed to determine what is going on: Did you disclose your overstay on the visa application? Did you experience any additional questioning when entering the country? What exactly did the EEA say when they refuse your application?

Also, what is your current nationality/citizenship and how much time has passed between your departure after overstaying and your application for a Z visa?

I'll try to simplify: I came 20 months ago to GZ, China for a 2-years postdoctoral research in GDUT university. I successfully applied for a working and residence permit. My chinese exgirfriend torn apart my passport with my residence permit on it. I got a new passport but at the university they assured me that I didn't need to apply for a re-print of the residence permit as long as I kept the torn apart passport (the residence permit could be perfectly read cause it was in two pieces). 3 months ago I went to HK and when I was about to return back to China they didn't let me in. I thus went to the border with Shenzhen and I applied for a 5 days visa. I thought that I could fix this issue in GZ and as the majority of the staff of the university where on vacations I overstayed 13 days with that visa. They didn't let me apply for a new residence permit in GZ. I went to Shenzhen, paid a fine and got a deportation visa. I tried to apply for a residence permit in GZ with this deportation visa but they didn't let me apply. I returned to Spain (I'm Spanish) got a Z visa and returned back to China last month. My university even extended my working permit but they couldn't make the appointment with the exit and entry bureau (the informatic systems says that I have an ongoing appointment). Thus I couldn't bring the updated application form (with my new working visa) to the exit and entry bureau. I'll try to explain them (at the exit and entry bureau) but they said that they could not help me and that the employer (GDUT) should be able to make the appointment. Then they started saying that it was because of the Shenzhen deporting visa I had before. I even applied for the non-criminal records and I have no records. So right now I'm not sure whether all of this is due to a bug in the system or I'm really blacklisted in China. Thanks for the help.

I didn't hide anything at the Chinese embassy in Spain. Actually I did not apply for a working visa on a conventional way (I brought a letter explaining my situation, show them my working contract, my valid work permit, etc.) but they granted me with a Z visa. When I entered China I had no issues at immigration. Thank you