I'm not sure there is some direct way, but you can iterate over sketches and get their names.
You can choose if you want to get sketches which directly use this parameter or select sketches which depends on this parameter. See and comment or un-comment lines 14, 15.
Test part is in attachment.
Sub Main()
Dim paramName As String = "Length"
Dim part As PartDocument = ThisDoc.Document
Dim parameterNames As New List(Of String)
'Direct parameter usage
parameterNames.Add(paramName)
'Parameter dependencies
'- Select one which best matches your needs
Dim param As Parameter = part.ComponentDefinition.Parameters.Item(paramName)
GetDirectDependencies(param, parameterNames)
GetAllNestedDependencies(param, parameterNames)
'Get sketch names
Dim sketchNames As String() = GetSketchNames(part, parameterNames)
'Print results
For Each sketchName As String In sketchNames
Logger.Debug(sketchName)
Next
End Sub
Private Sub GetDirectDependencies(param As Parameter, parameterDependencies As List(Of String))
For Each p As Parameter In param.Dependents.OfType(Of Parameter)
parameterDependencies.Add(p.Name)
Next
End Sub
Private Sub GetAllNestedDependencies(param As Parameter, parameterDependencies As List(Of String))
For Each p As Parameter In param.Dependents.OfType(Of Parameter)
parameterDependencies.Add(p.Name)
GetAllNestedDependencies(p, parameterDependencies)
Next
End Sub
Private Function GetSketchNames(part As PartDocument, parameterDependencies As List(Of String)) As String()
Dim sketchNames As New List(Of String)
For Each sketch As Sketch In part.ComponentDefinition.Sketches
For Each dimensionConstraint As DimensionConstraint In Sketch.DimensionConstraints
Dim parameterName As String = DimensionConstraint.Parameter.Name
If parameterDependencies.Contains(parameterName) Then
sketchNames.Add(Sketch.Name)
Exit For
End If
Next
Next
Return sketchNames.ToArray()
End Function