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JEMH velocity context, relating to emails (comment header specifically) has $sentDate (if present, reverts to now() if not) as well as $receivedDate. Presentation of these dates can be altered through helper classes in the velocity context.

Enterprise Mail Handler for Jira Data Center (JEMH) > Work with Dates in velocity templates > image2015-1-16 10:52:24.png

Lower down there are several date operators that are hyperlinked to API Documentation so you know what you can do with them:

Enterprise Mail Handler for Jira Data Center (JEMH) > Work with Dates in velocity templates > image2015-1-16 10:53:25.png

For example:

1a) $dateFormatter.format($sentDate)
1b) $dateFormatter.forLoggedInUser().withStyle($dateTimeStyle.RSS_RFC822_DATE_TIME).format($sentDate)
1c) $dateFormatter.forLoggedInUser().withStyle($dateTimeStyle.DATE_TIME_PICKER).format($sentDate)
1d) $dateFormatter.forLoggedInUser().withStyle($dateTimeStyle.RELATIVE).format($sentDate)
2) $outlookdate.formatDMY($sentDate) $outlookdate.formatTime($sentDate)
3) $dateformatter.getNow() / $dateformatter.formatIso8601($dateformatter.getNow()) 
4) $dateTimes.formatRSS($sentDate)

Generates:

1a) 16/Jan/15 10:47 AM
1b) Fri, 16 Jan 2015 10:47:48 +0000
1c) 16/Jan/15 10:47 AM
1d) Today 10:47 AM
2) 16/Jan/15 10:47 AM
3) Fri Jan 16 10:47:48 GMT 2015 / 2015-01-16T10-47
4) Fri, 16 Jan 2015 10:47:48 +0000

Velocity Custom Field Dates

JEMH can build date objects too, to enable values to be generated for arbitrary dates, e.g.:

Date Time

#set($longVal = $currentMillis.longValue() + 86400000 )
$dateFormatter.format($jemhDateUtils.createDate($longVal))

Example Output:

29/Mar/15 3:41 PM

Date Only

#set($longVal = $currentMillis.longValue() + 86400000 )
$dateFormatter.formatDMY($jemhDateUtils.createDate($longVal))

Example Output:

29/Mar/15

DatePicker custom fields

$dateFormatter.formatDatePicker($issue.getCustomFieldValue("customfield_10700"))

For further Date formatting options please see:

https://docs.atlassian.com/software/jira/docs/api/9.12.2/com/atlassian/jira/web/util/OutlookDate.html

JEMHDateUtils

JEMHDateUtils is another interface written by JEMH to accommodate certain functionality which is not achievable when working with Dates obtained from the email.

#set ($headerDate = "Wed, 19 Feb 2020 14:50:59 +0000")
#set ($dateFormat = "E, d MMM yyyy HH:mm:ss Z")
#set ($date = $jemhDateUtils.getZonedDateTime($headerDate, $dateFormat))
The date/time in the email is: $date.format($jemhDateUtils.getFormatter($dateFormat))

#set ($zone = $jemhDateUtils.getZoneId("America/Los_Angeles"))
#set ($laTime = $date.withZoneSameInstant($zone))
In Los Angeles this is: $laTime.format($jemhDateUtils.getFormatter($dateFormat))

Debugging velocity rendered custom fields as above is a bit tedious (issue JEMH-7794 logged to pick and evaluate script against a stored JEMH Test Case email). For rapid testing against a Test Case, you can do the same thing in a Script Field Processor edit window:

if (message.getHeader("Date") !=null)
{
 var headerDate = message.getHeader("Date")[0];
 var dateFormat = "E, d MMM yyyy HH:mm:ss Z";
 var date = jemhDateUtils.getZonedDateTime(headerDate, dateFormat);

print ('The date/time in the email is: ' +date.format(jemhDateUtils.getFormatter(dateFormat)) );

 var zone = jemhDateUtils.getZoneId("America/Los_Angeles");
 var laTime = date.withZoneSameInstant(zone);

print ('In Los Angeles this is: '+laTime.format(jemhDateUtils.getFormatter(dateFormat)) );
}
else
{
    print ('no Date: header');
}

The key functionality to note:

ZonedDateTime - we are using ZonedDateTime which allows us to retain the time zone aspect along with the date + time. This is vital aspect in case you’d wish to convert this to another time zone (which is what is being done in the above example)
Formatter - to format the date in a certain pattern (i.e. 12/02/2020 - 08:29), we have provided the getFormatter(pattern) method which is responsible for returning a DateTimeFormatter. The same can be used to format the ZonedDateTime to any other preferred format

Output:

The date/time in the email is: Wed, 19 Feb 2020 14:50:59 +0000
In Los Angeles this is: Wed, 19 Feb 2020 06:50:59 -0800

Creating relative dates in custom fields

@since 3.3.27

This set of methods doesn’t depend on any Jira user in the authentication context, e.g., you want to do date/time manipulation for a custom field default

See formatter parameters here: https://docs.oracle.com/javase/8/docs/api/java/time/format/DateTimeFormatter.html

$jemhDateUtils.createLocalDate().plusDays(15).format($jemhDateUtils.getFormatter("dd/MMM/yy"))

If you want to use the Jira format: