Seattle-based Judge John Coughenour requested the firm to run the discount procedure for 12 months starting in January 2017.
It takes after effective legitimate activity by the US Federal Trade Commission (FTC).
However the FTC's require a knot discount of $25.6m (£20m) was rejected.
Judge Coughenour said the figure was "too high", Reuters reported.
He likewise turned down Amazon's ask for to offer repayment as blessing cards.
The choice of paying for additional substance inside versatile applications, for example, diversions and music stages was propelled by Amazon and different stages in 2011.
Guardians griped that it was too simple for youngsters to make buys, either unintentionally or without authorisation, while playing diversions.
The FTC propelled legitimate activity in 2014.
"At the point when Amazon acquainted in-application accuses of the Amazon Appstore in November 2011, there were no secret key necessities of any sort on in-application charges, incorporating into children's diversions and different applications that interest to kids," it said at the time.
It likewise gave the case of a diversion called Ice Age Village, in which youngsters could utilize free "oak seeds" or "coins" as cash but at the same time could buy a greater amount of them with genuine cash in a scene that was "outwardly comparative" to the free trade.
Since 2014, Amazon has changed how in-application buys are depicted in its application store and refined its authorisation encounter.
In-application buys can be crippled totally with the organization's parental control alternatives.
When it sued Amazon in 2014, the FTC likewise propelled lawful activity against Apple and Google.
In particular settlements Apple consented to discount clients more than $30m (£20m) and Google about $19m (£13m).
The judge ruled against Amazon in April 2016 and has now issued the discount arrange.
The FTC and Amazon have been reached by the BBC for input.