The residence permit according to paragraph 25 Abs. 5 is issued at first in three periods of 6 months. Once these 18 months have passed, the Ausländerbehörde can issue a permit with a longer validity up to a maximum of three years. Once you have resided in Germany with a residence permit for five years, you can apply for permanent residency (unbefristet, Niederlassungserlaubnis), as long as other requirements are fulfilled.
In general, a person applies for a residence permit to be issued or renewed. It is the Ausländerbehörde who decides how long to grant a person a permit for, rather than the person requesting a certain amount of time. When applying to renew your permit, you can make reference to paragraph 26 Abs 1 and request that they issue you with a permit for a certain period. I cannot say, however, whether that will have any influence on their decision. Most likely they have a standard practice where a person who has completed the three periods of 6 months on the 25,5 permit then receives a permit of one or two years.