مَدْرَسَةٌ means school. It has a final tāʾ marbūṭa, but it is a common noun rather than a proper name, so it is normally fully declinable.
هٰذِهِ مَدْرَسَةٌ — This is a school: the predicate is nominative with tanwīn.
دَخَلْتُ مَدْرَسَةً — I entered a school: the object is accusative with tanwīn.
مَرَرْتُ بِمَدْرَسَةٍ — I passed by a school: the noun after the preposition is genitive with kasra and tanwīn.