Word Choice – ‘In the Outskirts’ vs ‘On the Outskirts’ Explained

The preposition that goes with "occasion" is usually "on", and never "at" (unless by "occasion" one means an event or gathering, which is not the case here), so "On various occasions" sounds more natural. Note, similarly, that we can also say:

I like to eat broccoli on occasion.

but never:

I like to eat broccoli at occasion.

I would also suggest "many times" or "several times" as alternatives to "on various occasions".

1a is ungrammatical. In the subsequent examples the difference is that another is more definite. By using some other, the speaker or writer is making a reference so vague that there is some doubt over whether the statement in which it occurs can be true.