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We construct a special class of fermionic Novikov superalgebras from linear functions. We show that they are Novikov superalgebras. Then we give a complete classification of them, among which there are some non-associative examples. This method leads to several new examples which have not been described in the literature.

We prove that there are at least two new non-naturally reductive $\mathrm{Ad}\left(\mathrm{Sp}\right(l)\times \mathrm{Sp}(k)\times \mathrm{Sp}(k)\times \mathrm{Sp}(k\left)\right)$ invariant Einstein metrics on $\mathrm{Sp}(l+3k)$ $(k<l)$. It implies that every compact simple Lie group $\mathrm{Sp}\left(n\right)$ for $n=l+3k>4$ admits at least $2\left[\frac{1}{4}(n-1)\right]$ non-naturally reductive $\mathrm{Ad}\left(\mathrm{Sp}\right(l)\times \mathrm{Sp}(k)\times \mathrm{Sp}(k)\times \mathrm{Sp}(k\left)\right)$ invariant Einstein metrics.