RestAPI Alerts access to ExternalTicketID

I'm using X-Version=3 as well.  Looks like you're using PowerShell, here's a snippet that's working for me.

$company = "your-lm-company"  # Replace with your LogicMonitor company name
$bearerToken = "your-lm-bearer-token" # replace with your LM bearer token
$daysAgo = 2  # Number of days to look back for alerts

# calculates the epoch time for the start of the query
$startEpoch = (Get-Date (Get-Date).AddDays(-$daysAgo) -UFormat %s) 

# query string includes the ##EXTERNALTICKETID# custom column and filters for alerts created after the startEpoch.  
# This Will get the first 1000 results, you'll need to put a loop in to handle paging if you expect  more than that.
$queryString = ('?customColumns=%23%23EXTERNALTICKETID%23%23&size=1000&offset=0&filter=startEpoch>:' + $startEpoch)

$headers = New-Object "System.Collections.Generic.Dictionary[[String],[String]]"
$headers.Add("Authorization","Bearer $bearerToken")
$headers.Add("X-Version",'3')
$headers.Add("Content-Type",'application/json')

$alerts = (Invoke-RestMethod -Uri "https://$company.logicmonitor.com/santaba/rest/alert/alerts$queryString" -Method "GET" -Headers $headers).items

# Filter the alerts to only include those that went to a rule where the name includes "Service Now" and that were not suppressed (e.g. not SDT at the time)
# Does a bit of manipulation to extract the ServiceNow Incident ID from the custom column ##EXTERNALTICKETID##
$alerts | where-object {$_.rule -like "*Service Now*" -And !($_.suppressor)} | Select-Object `
    @{Name="Alert ID";Expression={$_.id}}, `
    @{Name="InternalId";Expression={$_.InternalId}}, `
    @{Name="External_Ticket_ID_RAW";Expression={$_.customColumns.'##EXTERNALTICKETID##'}}, `
    @{Name="SNOWIncidentId";Expression={$_.customColumns.'##EXTERNALTICKETID##'.split(':')[1].trim()}}, `
    @{Name="SNOWLinks";Expression={$_.alertExternalTicketUrl.'servicenowIncidentLinks'}}

You'll need to change (or remove) the filter I've put in for $_.rule -like "*Service Now*" to match whatever your rules are.  You should get something like the output below.

Alert ID               : DS8871637
InternalId             : LMD33542811
External_Ticket_ID_RAW : ServiceNow xxxx : INC5147309
SNOWIncidentId         : INC5147309
SNOWLinks              : @{INC5147309=https://xxxxx.service-now.com/now/nav/ui/classic/params/target/incident.do%3Fsys_id%3D82fa6f601bb22a507f1da608b04bcbb9}

Alert ID               : DS8871639
InternalId             : LMD33542820
External_Ticket_ID_RAW : ServiceNow xxxxx : INC5147311
SNOWIncidentId         : INC5147311
SNOWLinks              : @{INC5147311=https://xxxxx.service-now.com/now/nav/ui/classic/params/target/incident.do%3Fsys_id%3Dab1b27241b766ad006c94043b24bcb1e}

Alert ID               : DS8871640
InternalId             : LMD33542817
External_Ticket_ID_RAW : ServiceNow xxxxx : INC5147312
SNOWIncidentId         : INC5147312
SNOWLinks              : @{INC5147312=https://xxxxx.service-now.com/now/nav/ui/classic/params/target/incident.do%3Fsys_id%3Dfd7b6b241bb22a507f1da608b04bcb49}