tl;dr

myPreparedStatement.setObject( 
    … , 
    OffsetDateTime.parse( "2006-02-16T21:36:32.000+0000" )  
) 

With and without zone/offset

You said your column is of type TIMESTAMP which is short for TIMESTAMP WITHOUT TIME ZONE. This type purposely lacks any concept of time zone or offset-from-UTC. Not usually appropriate for common business purposes.

You are using wrong type

That is the wrong type for your input. Your input has an offset-from-UTC of zero hours which means UTC itself. Having an offset or zone, your data should only be stored in a TIMESTAMP WITH TIME ZONE type column. In this …WITH… type in Postgres, any submitted offset/zone info is used to adjust into UTC for storage, and then discarded.

Storing a date-time value with an offset or zone in a column of type TIMESTAMP WITHOUT TIME ZONE is like storing a price/cost with a designated currency( USD, Euros, Rubles, etc.) in a column of numeric type. You are losing vital data, the currency. This renders your data worthless.

See the Postgres documentation page for these types.

Smart objects, not dumb strings

Whenever possible, use objects to exchange data with your database rather than passing meter strings. Let your JDBC driver do it’s job in marshaling the data back-and-forth.

Parse the input string as an OffsetDateTime object.

ISO 8601

Your input strings are in a format defined by the ISO 8601 standard. The java.time classes use ISO 8601 formats by default when parsing/generating strings. No need to specify a formatting pattern.

String input = "2006-02-16T21:36:32.000+0000" ;
OffsetDateTime odt = OffsetDateTime.parse( input ) ;

Define your SQL as a prepared statement.

With JDBC 4.2 and later, you can directly exchange java.time objects with your database. No need to ever again use the troublesome legacy classes such as java.sql.Timestamp.

You could pass an OffsetDateTime. I like to extract an Instant to demonstrate to the reader that I understand how Postgres always stores a TIMESTAMP WITH TIME ZONE value in UTC.

Instant instant = odt.toInstant() ;
myPreparedStatement.setObject( … , instant ) ;

Retrieval.

Instant instant = myResultSet.getObject( … , Instant.class ) ;