How to convert integer xml value to JSON without quotes

XML is text-based, so any values you extract from an [xml] (System.Xml.XmlDocument) document will be strings.

^{To quote from Mathias R. Jessen's comment on the question: "The XML specification is pretty clear about this: Only string literals and references can be used as attribute values, and they must be delimited using single- or double-quotes."}

If you want those values to be other types, you must perform explicit conversions.

Passing such converted values to ConvertTo-Json will then automatically omit the quotes if they are of a type that is represented unquoted in JSON (numbers, null, true and false)

In the case at hand, you can use -as, the conditional type conversion operator, to conditionally convert a string to an integer, if it can be interpreted as such:

# Sample XML input.
# Note the two "Value" attribute values, "test1" and "42".
[xml] $xmlDoc = @'
<?xml version="1.0" encoding="utf-8"?>
<Application xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" Name="application" xmlns="http://schemas.microsoft.com/2011/01/fabric">
  <Parameters>
    <Parameter Name="Parameter1" Value="test1" />
    <Parameter Name="parameter4" Value="42" />
  </Parameters>
</Application>
'@ 
  
# Transform the "Parameter" elements into a nested hashtable.
# Convert any values that can be interpreted as [int] to [int].
$hash = [ordered] @{}
$xmlDoc.Application.Parameters.ChildNodes | ForEach-Object {
  $hash[$_.Name] = @{
    # Convert the text value to an [int], if it can be parsed as such.
    value = if ($num = $_.Value -as [int]) { $num } else { $_.Value }
  }
}

# Wrap the hashtable in a top-level hashtable and convert to JSON.
[ordered] @{
  '$schema' = 'https://schema.management.azure.com/schemas/2015-01-01/deploymentParameters.json#'
  contentVersion ='1.0.0.0'
  parameters = $hash
} | ConvertTo-Json

The above yields the following: note how 42 is unquoted:

{
  "$schema": "https://schema.management.azure.com/schemas/2015-01-01/deploymentParameters.json#",
  "contentVersion": "1.0.0.0",
  "parameters": {
    "Parameter1": {
      "value": "test1"
    },
    "parameter4": {
      "value": 42
    }
  }
}