See Log::Log4perl::Layout::PatternLayout and Log::Log4perl::DateFormat and use %d{Z}

#!/usr/bin/perl --

use strict;
use warnings;

use Log::Log4perl 1.26 qw(:easy);


my $logconfig = <<"__LOGCONFIG__";
log4perl.rootLogger = ALL, First
log4perl.appender.First = Log::Log4perl::Appender::Screen
log4perl.appender.First.layout = Log::Log4perl::Layout::PatternLayout
log4perl.appender.First.layout.ConversionPattern= %d{yyyyMMdd.hhmmss:Z
+}-%P-%%H-%p{2}-%m%n
__LOGCONFIG__

Log::Log4perl::init( \$logconfig );

DEBUG('debug');
INFO('info');
WARN('warn');
ERROR('error');
TRACE('trace');
FATAL('fatal');

__END__
20160302.102316:-0800-3608-%H-DE-debug
20160302.102316:-0800-3608-%H-IN-info
20160302.102316:-0800-3608-%H-WA-warn
20160302.102316:-0800-3608-%H-ER-error
20160302.102316:-0800-3608-%H-TR-trace
20160302.102316:-0800-3608-%H-FA-fatal
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