This is not a question but just reporting on my case of applying to an early C permit because nowhere in the forum I found a similar case and I thought it might be useful to share here.
I (non-EU/Egyptian) came to Switzerland in October 2015 for PhD studies (with a working student B permit) and graduated in September 2018.
While my B permit was still valid, an official gave me the unfavorable recommendation to get the L permit that graduates get for job search (Stellensuche) as my B permit was void with finishing the studies. So I got the L permit in November 2018 but it was issued for 4 months only because my graduation was in September 2018.
Thankfully, I found a job (permanent contract) in December and started working in February 2019. My work permit was authorized in February so I started working while still on the L permit. In March 2019, my unlimited B permit was issued.
I was reading a lot about early application to B permit and that study years can be counted towards the 5 years if the graduate has B permit for work for at least 2 years.
But as you might have gathered, my problem was that I had an L permit. People would read the law and the requirement for the early granting of C permit which is "5 uninterrupted years with B permit" and most would understand it as having B permit continuously for 5 years. This would make me ineligible for the early C permit.
I asked the employee responsible for my file in the migration office of Basel in early 2020 and he said that I am not eligible.
In early October 2020, I thought of asking again and told him that one might understand the law as "uninterrupted stay" with 5 years of B permit regardless of any gap in the middle and I argued with him that I abided by the law and asked for the L permit while my B permit was valid so this doesn't necessarily make my stay on the L permit of a temporary nature because it is with the goal of finding a job and staying in the country. So, he said that he will ask his manager and let me know. He did and in a few days he wrote me an email saying that I "can apply for the early C permit with pleasure". The requirements from Basel were only a language certificate (B1 oral and A2 writing) and copies of the work contract and last 3 salary slips.
Having only 3 months before the time for my application for permit renewal, I booked a TELC test in Freiburg, Germany in the last week of November (thankfully the border was not closed yet) because it is corrected faster than in Switzerland. The certificate arrived in Basel in the second week of January (293/300). Meanwhile, I had received the permit renewal form which I got signed and stamped from my employer.
In addition to what the migration office asked for, I also got the documents showing that I don't have any outstanding debt, didn't commit a crime and didn't receive social help. I also wrote a long letter clarifying my contribution to the economic life in Basel and Switzerland (including an estimate number of the taxes that I paid in the previous 5 years). I sent all of these documents to the migration office in Basel during the last week in January 2021.
Two weeks passed and I contacted the responsible person and he hadn't received my documents yet because he had worked from home. I tried to contact the migration office again in the third week of February and it appeared in the system now that he received the documents and started working on them. One week later, I tried to contact him and my file was still in progress. That was on the 25th of February and my permit expires on the 9th of March!!
On the 26th of February, I phoned the office again and he was there on that day and said that he will finalize my file later on the same day and send it to SEM as the request for early C permit is subject to their approval.
So, on the same day afternoon, he indeed emailed me confirming that my file was sent to SEM.
YAAAYYYY! One milestone reached - Cantonal approval!
Now it is less than a week and my permit is going to expire. I called SEM in the morning of the 3rd of March and the employee on phone confirmed that they received my file and said that she would notify the responsible employee at SEM to work on it urgently. In the afternoon of the 4th of March, after 1.5 hours of trying to call SEM but getting a busy signal, they picked up and confirmed that the C permit was approved!! They asked me to contact the cantonal migration office for the next steps.
End of Story!!
Morale of the story: persistence!