"of" vs"in" which preposition is more suited in the below context?

With those words, you would probably say ‘stoppage of development’. With ‘the development’ it would normally be ‘in the development’ but ‘stoppage’ is normally with ‘of’ so this creates a slight artistic clunkiness which would not be resolved. If necessary I would say ‘stoppage in the development’ however it is not perfect.

They seem equally suitable.

Compare:

• The penalty caused a stoppage in play.

• During the stoppage of bus service he drove to work.

• The stoppage of exports shouldn’t last long.

There are many more examples easily found via Google. It seems that stoppage of is by far more common, though that doesn't preclude usage of stoppage in.

You do need to give a context for your question. Without this, it is difficult to tell which if either of your two sentences is correct. One particular thing I cannot tell is whether you are asking about American or British English. My answer is based on British English. In British English, the word stoppage presupposes that someone has stopped something. So the first definition in the Cambridge English Dictionary is as follows.

A time when work is stopped because of a disagreement between workers and employers.

In addition, it gives other uses more commonly found in US and Antipodean English.

1. (of money). an amount that is taken away from the money that you are paid before you officially receive it.
   for example: Stoppages include things like pension contributions and national insurance

2. (in football - ie soccer). a time during a football match when the game is stopped because of an injury to a player: for exampleIn a cup final, if the teams are level after 90 minutes plus any time added on for stoppages, they play extra time.

Your use of the word does not fit any of these definitions, and so the question of which prepositions should be used does not arise. In medical jargon, in relation to physical or mental development, the expression is 'arrested development'. Sometimes the term 'delayed' is also used in a similar context. 'Stoppage', however, it is used, will tend to mean a temporary stop, or interruption. So it can easily apply to human activities, and so be the effect of human decisions.

Wikipedia has an article on 'arrested development' in which the term stoppage is used in the definition!

Coming back to the sentence you are asking about, you do not need any preposition. Instead, you can write:

He suffers from delayed (or arrested) physical development.

The first of these two (delayed) would mean he is not as physically developed (perhaps in one of his limbs?) or mentally developed (perhaps in literacy, or social interaction) as most other children/people. The term retarded used to be used here of mental development, but became a term of scorn or abuse and so rightly abandoned. The term arrested development indicates that some development is incomplete.

As to the right preposition for your three example sentences, Touchstone in his/her answer gives a reasonable answer.

1- There is a stoppage in the development = There is a stoppage within/inside/during the development.

2- There is a stoppage of the development = There is a stoppage associated with the development.