Mathematical symbol for 'slightly greater than'?

More often it is used as $b=a+\epsilon$ where $\epsilon$ normally stands for a small positive quantity. That provides b slightly greater than a. Similarly $-\epsilon$ for slightly below.

Perhaps:

$$\lt_\epsilon\quad\gt_\epsilon\quad\lt^\epsilon\quad\gt^\epsilon$$

using the idea that $a\lt^\epsilon b$ means $a+\epsilon=b$, where $\epsilon\gt0$.

No. There isn't such a symbol.