"doubts over" is correct and can be used in written English.
It can be used when expressing uncertainty or suspicion concerning something. For example, "There are doubts over the validity of his claims".
There are also doubts over Cruyff's position.
No doubts over who committed the town's latest murder.
Doubts over corporate credibility still weighed on the market.
The clause is sufficiently ambiguous to leave doubts over how the stalemate will be resolved.
Doubts over whether China can still meet its full-year economic growth target have increased.
Yet as the date looms, doubts over whether the talks will start keep recurring.
The Archbishop of Canterbury has admitted to feeling doubts over the existence of God.
There were initial doubts over whether the crowds would be allowed on the iconic hill.
Small wonder that all three voiced strong doubts over the American-British plans.
If there were doubts over the first score, there were none for his second.
But Britain has long opposed carbon taxes, raising doubts over whether the tax could win approval.
