The detection of local maxima in a spectrum is limited to the DFT support points without further processing. The following example shows this for a 25 Hz sinusoid at a sampling rate of 100 Hz.
Quadratic or parabolic interpolation can be used to estimate the true peak of the sinusoid. using the detected maximum $a$ and its upper and lower frequency bin.
$p = 0.5 (\alpha-\gamma)/(\alpha-2\beta+\gamma)$
$a^* = \beta-1/4(\alpha-\gamma)$