Temporary proof of German Residence

To stay in Germany longer than 90 days in a 180 period, you will need a residence permit. Qualifying for a residence permit will depend, among other things, on the type of visa you applied for. Your long-stay visa allows you to travel to Germany. Within two weeks after arrival in Germany, you need to register at your local town office and Immigration authority. See Registering at the local town office. You will receive a Meldebestätigung (Certificate of registration at the main residence)

After registering at the relevant immigration authority (Ausländerbehorde), you will be issued a Residence permit.

Fiktionsbescheinigung

Due to circumstances, it can take longer than expected to receive your residence permit card. The current process is that the Ausländerbehorde send your papers to the Staatsdrükerei in Berlin, who has to print your Residence card. This is then sent back to the Ausländerbehorde and they will contact you to come pick it up.

If you need proof of residence, for example, to travel, you can request a fictional certificate or Fiktionsbescheinigung at the Ausländerbehörde, which they can issue immediately,

This document is seen as proof of your residence permit and will have the same restrictions as your residence permit. This could be a single entry or if you are allowed to work.
A single entry will mean you are not permitted to travel back to Germany unless otherwise indicated.
A fictional certificate cannot be issued to holders of a Schengen visa for short-term residence (Category C).

§ 81 Abs. 4 of the AufenthG

If a foreigner applies for an extension of his or her residence title or for a different residence title before his or her current residence title expires, the current residence title is deemed to remain in force from the time it expires until the time of the decision by the foreigner’s authority. This does not apply to visas issued in accordance with section 6 (1). If the application to issue or extend a residence title was filed too late, the foreigner’s authority may order that the previous residence title remains valid in order to avoid undue hardship. – Gesetze im Internet

From Service Berlin
If a currently valid residence permit (temporary residence permit or national visa for long-term durations – Category D ) is available, a fictional certificate according to § 81 Section 4 of the Residence Act will be issued. In this case, the residence permit and all supplementary regulations (also regarding the stipulations concerning gainful employment) remain in force until a decision has been made in relation to the application. Journeys abroad and re-entry into the area of the Republic are possible with a valid fictional certificate in accordance with § 81 Section 4 of the Residence Act.

§ 81 Abs. 3 of the AufenthG

If a foreigner who is legally resident in the federal territory and does not possess a residence title applies for a residence title, his or her residence is deemed to be permitted up to the time of the decision by the foreigners authority. If the application is filed too late, deportation is deemed to be suspended from the time of application up to the time of the decision by the foreigners authority. – Gesetze im Internet

From Service Berlin
If the male or female applicant is lawfully resident without a visa in the Federal Republic, because he or she is entitled to be by virtue of his/her nationality, the fictional certificate will be issued in accordance with § 81 Section 3 of the Residence Act.
This permits residence in the area of the Federal Republic until a decision has been made regarding the application. This fictional certification, however, does not permit re-entry into the territory of the Federal Republic. It also does not permit the commencement of gainful employment.