The correct option is
C turn down
The phrasal verb, 'turn down' when used along with the words, 'radio' or 'television' or 'heater' means '
reduce the amount of sound or heat being produced, by adjusting the control'. The phrasal verb, 'turn up', means the opposite of the word, 'turn down' when used along with the word, 'radio'. When we read the second sentence along with the first sentence, we understand that it is late in the night and the speaker is trying to sleep. However, the sound arising from the radio is disturbing him. Hence, the appropriate phrase to be used is 'turn down' i.e reduce the volume of the radio. The phrase 'turn up' is not appropriate because increasing the volume of the radio would disturb the speaker further. Hence, option B is correct and option A is incorrect.
The phrasal verb 'turn over' means 'hand something to someone'. Eg: The witness turned over the physical evidence of the theft to the police'. Given this meaning, option C is incorrect.
The phrasal verb 'turn off' means 'switch off'. While switching off the radio would give relief to the speaker and allow him to sleep, this is not appropriate in the given sentence. This is because, the phrase, 'a little' has been used. A radio can either be 'switched off' or 'switched on'. It is not possible to switch off a radio 'a little'. Hence, option D is incorrect.