The Private scope may be accessed using the private prefix, as follows:

$private:thisValue = "Some value" 

Moving a variable into the Private scope will hide the variable from child scopes:

Remove-Variable thisValue -ErrorAction SilentlyContinue 
# This is still "local" scope 
$private:thisValue = "Some value" 
"From global: $global:thisValue"           # Accessible 
 
function Test-ThisScope { 
    "Without scope: $thisValue"            # Not accessible
     "From private: $private:thisValue"     # Not accessible 
    "From global: $global:thisValue"       # Not accessible 
} 
 
Test-ThisScope 

If the stack depth is increased, the variable search can be made to skip a private variable within an intermediate function and reference the variable from an ancestor, as shown here:

PS> function bottom {
    $thisValue = "Bottom"
    Write-Host "Bottom: $thisValue"
    middle
} 
function middle {
    # Hide thisValue from children
    $private:thisValue = "Middle" # Middle only
    Write-Host "Middle: $thisValue"
    top
}
function top {
    Write-Host "Top: $thisValue" # Original value
}
bottom

Bottom: Bottom
Middle: Middle
Top: Bottom