In the next year vs. For the next year vs. Over the next year

Solution 1:

In the next year = at some time in the next 12 months. "I plan to start learning French in the next year."

For the next year = for the whole of the year. "Mr Smith was elected chairman for the next year."

Over the next year could mean the same, or at intervals during the year. "He will chair ten meetings over the next year."