Is there a way to override the Local time Zone with Specified TimeZone while getting Epoch value.
No. You can generate a timestamp for any supported IANA representative location, but you can't "set a timezone" for the Date instance itself.
ECMAScript Date objects are just a time value that is an offset in milliseconds from 1 Jan 1970 UTC. They have no timezone and can only work in either the local timezone or UTC, that's it. When parsing a timestamp for a particular timezone, the result is a UTC time value. That is the only thing the Date instance remembers so it doesn't matter how you generate a Date, the time value is always effectively UTC.
The plain get and set methods like getYear, getMintues, etc. and the toString methods use the UTC time value and host settings to generate local date and time values. The UTC get and set methods like getUTCYear, getUTCMintues, etc. and toISOString, toUTCString etc. return UTC values. So you can work in either local or UTC, working in some other timezone or location requires you to do the work (which is quite complex and likely a library is a better option).
You can get a timestamp for any supported IANA representative location using toLocaleString with the timeZone option, however that only affects the generated string, it doesn't change the underlying UTC time value.
You can't set a timezone or location for a Date object as it doesn't have any property on which to set it, it's just a (UTC) time value, that's it.
Also, the built–in parser is not required to parse the output from toLocaleString, primarily because the user can configure the output to a huge number of different formats that may not include any date or time values (e.g. you can get just the timezone or offset). So depending on parsing such values is fundamentally flawed.