Question

Identify the figure of speech:
'And in my humorous way,I added(as a trifling jest)'

Answer 1

I would say, this sentence is an example of hyperbaton or inversion.

'And, in my humorous way,I added(as a trifling jest)'

Hyperbaton (Greek word for "overstepping") consists in the inversion or transposition of the normal grammatical order of words in a sentence for the sake of emphasis. Some elements or regular syntax overstep others.

According to the blog of Oxford Dictionaries,

                                               "The argument against using ‘and’ or ‘but’ to introduce a sentence is that such a sentence expresses an incomplete thought (or ‘fragment’) and is therefore incorrect."

The proper syntactical order of this above mentioned sentence would be, "I added in my humourous way....(the object) as a triflling jest"

Answer 2

The figure of speech used here is a simile.

It is  a figure of speech that involves comparison between often two very dissimilar objects, which however, have one point of similarity or at least one point in common.

Generally as or like is used as a part of simile to point out how one thing looks like the other, or how one thing is as the other thing.

For example, he is as cool as cucumber.