tl;dr

ZonedDateTime.parse( 
                        "Jun 13 2003 23:11:52.454 UTC" , 
                        DateTimeFormatter.ofPattern ( "MMM d uuuu HH:mm:ss.SSS z" ) 
                    )
              .toInstant()
              .toEpochMilli()

1055545912454

java.time

This Answer expands on the Answer by Lockni.

DateTimeFormatter

First define a formatting pattern to match your input string by creating a DateTimeFormatter object.

String input = "Jun 13 2003 23:11:52.454 UTC";
DateTimeFormatter f = DateTimeFormatter.ofPattern ( "MMM d uuuu HH:mm:ss.SSS z" );

ZonedDateTime

Parse the string as a ZonedDateTime. You can think of that class as: ( Instant + ZoneId ).

ZonedDateTime zdt = ZonedDateTime.parse ( "Jun 13 2003 23:11:52.454 UTC" , f );

zdt.toString(): 2003-06-13T23:11:52.454Z[UTC]

Count-from-epoch

I do not recommend tracking date-time values as a count-from-epoch. Doing so makes debugging tricky as humans cannot discern a meaningful date-time from a number so invalid/unexpected values may slip by. Also such counts are ambiguous, in granularity (whole seconds, milli, micro, nano, etc.) and in epoch (at least two dozen in by various computer systems).

But if you insist you can get a count of milliseconds from the epoch of first moment of 1970 in UTC (1970-01-01T00:00:00) through the Instant class. Be aware this means data-loss as you are truncating any nanoseconds to milliseconds.

Instant instant = zdt.toInstant ();

instant.toString(): 2003-06-13T23:11:52.454Z

long millisSinceEpoch = instant.toEpochMilli() ; 

1055545912454

About java.time

The java.time framework is built into Java 8 and later. These classes supplant the troublesome old legacy date-time classes such as java.util.Date, Calendar, & SimpleDateFormat.

To learn more, see the Oracle Tutorial. And search Stack Overflow for many examples and explanations. Specification is JSR 310.

The Joda-Time project, now in maintenance mode, advises migration to the java.time classes.

You may exchange java.time objects directly with your database. Use a JDBC driver compliant with JDBC 4.2 or later. No need for strings, no need for java.sql.* classes. Hibernate 5 & JPA 2.2 support java.time.

Where to obtain the java.time classes?

• Java SE 8, Java SE 9, Java SE 10, Java SE 11, and later - Part of the standard Java API with a bundled implementation.
  • Java 9 brought some minor features and fixes.
• Java SE 6 and Java SE 7
  • Most of the java.time functionality is back-ported to Java 6 & 7 in ThreeTen-Backport.
• Android
  • Later versions of Android (26+) bundle implementations of the java.time classes.
  • For earlier Android (<26), the process of API desugaring brings a subset of the java.time functionality not originally built into Android.
    • If the desugaring does not offer what you need, the ThreeTenABP project adapts ThreeTen-Backport (mentioned above) to Android. See How to use ThreeTenABP….

  String dateTime="15-3-2019 09:50 AM" //time should be two digit like 08,09,10 
   DateTimeFormatter dtf  = DateTimeFormatter.ofPattern("dd-MM-yyyy hh:mm a");
        LocalDateTime zdt  = LocalDateTime.parse(dateTime,dtf);
        LocalDateTime now = LocalDateTime.now();
        ZoneId zone = ZoneId.of("Asia/Kolkata");
        ZoneOffset zoneOffSet = zone.getRules().getOffset(now);
        long a= zdt.toInstant(zoneOffSet).toEpochMilli();
        Log.d("time","---"+a);

you can get zone id form this a link!