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Fermions are particles with an intrinsic angular momentum (i.e. spin) equal to a "half integer" number of fundamental units: $\frac{(2n+1)}{2} \hbar$ for integer $n$. Fermions are required to be in a quantum state that is globally anti-symmetric, which leads to the Pauli Exclusion Principle barring identical fermions from occupying the same quantum state.
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Fermionic partition function
When we calculate the fermionic partition function, we use $\newcommand{\ket}[1]{| #1 \rangle}
\newcommand{\bra}[1]{\langle #1 |} \newcommand{\braket}[1]{\langle #1 \rangle}$
$Z=tr(e^{-\beta H})=\int …