Praise be to Allah.
If a person believes that his fast has been spoiled, then he refrains from eating out of respect for the sanctity of the month, then it becomes clear to him that his fast was not spoiled, then he does not have to make up that day, and the fact that he believed his fast to have been spoiled does not affect it, because he did not do anything that cancelled out the fast and he did not intend to break the fast.
We have previously explained that the more sound scholarly view is that if someone becomes uncertain whilst fasting, as to whether he wants to break the fast or not, then his fast remains valid, and he does not break the fast merely by thinking (of whether to break the fast of not), so long as he had started to fast and embarked upon the fast with a firm intention, and has not done anything to render his fast invalid. That is because the basic principle is that the fast remains valid, and uncertainty as to whether one wants to break the fast or not does not undermine the initial intention (niyyah) of fasting, unless he firmly resolves to break his fast.
This was stated in fatwas issued by Shaykh Ibn ‘Uthaymeen and Shaykh Ibn Jibreen (may Allah have mercy on them both).
See the answer to question no. 194641
But if this is the case with regard to one who was uncertain whether to break his fast or complete it, then it is more appropriate to say that the fast of one who never thought of breaking the fast in the first place and never did anything to render his fast invalid – and all that he did was to complete his fast out of respect for the sanctity of the month – is valid and sound.
Conclusion: this fast is valid, and it counts as the obligatory fast that he intended to observe, and he does not have to do anything.
And Allah knows best.