Single parents in need can request an additional benefit (in accordance with § 21 Para. 3 SGB II (German Social Code)) of 155,52 € if they live with a child under seven or with two or three children under 16 (or 51,84 € with a child over seven) and are solely responsible for looking after and raising the child. Persons in need are deemed as those earning an income just above the requirement in German Social Code Volume II (standard rate plus appropriate rent including heating). See information on § 27 SGB II (see 27 - Leistungen für Auszubildende).
Additional benefits cannot be used by students with a residency permit as per § 16 of the German Residence Act!
The Counselling Centre for Social & International Affairs – BeSI also offers advice on this.