I have to use a particular sentence which is:
They differ at at least one position.
Is this the correct use of at least? Is my sentence correct?
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The "at at least" word string is not inherently impossible. For example:
Her little dog, Toto, has snapped at at least three bicyclists in the past month.
As other answerers have pointed out, the phrase "differ at" may sound less natural than "differ on" or "differ in" in the sentence "They differ in/on/at/from at least one position," depending on what the position in question refers to. Still, I can imagine a scenario where "differ at" might be the strongest choice. Suppose that you are comparing two baseball teams that have similar strengths and weaknesses, except that one has a much better third baseman than the other. Then you might sum up your comparison by saying
Both teams are strong up the middle, have serviceable starting rotations and excellent relievers, hit for power but not average, and have a fairly strong bench. They differ at at least one position, however: third base.