I devote much of time . . . . . . . . writing.

The other prepositions are not as appropriate in this context.

• The preposition in is used to indicate a location or position. In this case, it would not make sense to say that the speaker devotes much of their time in writing.
• The preposition on is used to indicate a surface or area. In this case, it would not make sense to say that the speaker devotes much of their time on writing.
• The preposition at is used to indicate a time or place. In this case, it would not make sense to say that the speaker devotes much of their time at writing.