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.

The "much greater" symbol $\gg$ is not exactly standard and should always come with an explanation.

There is no standard symbol for "slightly greater". It is the kind of thing best explained in English or made precise mathematically, as suggested by AHusain