Question

incidentally means :
by the way (used to introduce a new topic)
with obstinate determination and perseverance
in addition; by way of addition; furthermore
in such a manner as could not be otherwise

Explanation:

The word "incidentally" is an adverb. In common usage, it is often used to introduce a new topic or to mention something in passing. This is in line with the meaning "by the way (used to introduce a new topic)". The other options do not match the typical definition of "incidentally". "With obstinate determination and perseverance" is more related to words like "doggedly". "In addition; by way of addition; furthermore" is more like "additionally" or "moreover". "In such a manner as could not be otherwise" is not the meaning of "incidentally".

Answer:

by the way (used to introduce a new topic)