Esoterically means “in an esoteric way”: spoken, written, or done so that only a few people with special knowledge can follow. A scientist might explain a result esoterically, packing the sentence with field words. You form it from the adjective esoteric plus -ally, the usual English way of making this kind of adverb (like “basic” → “basically”). It is uncommon in speech; you will meet it more in writing. Though actually, if a simpler phrase such as “in a very specialist way” would do, many teachers would choose that for new readers — the long adverb is the precise one when you want to keep the “inner circle” feel.