First, please do yourself a favor and use strict;

This shouldn't work as expected since $ip is not expanded (remove the quotes): $t =Net::Telnet::Cisco->new(Host=>$ip);

When you try to connect/telnet to 192.168.201.3 and the error message is port:23 not connected, that's not a Perl problem, but a network connectivity problem (no telnet-daemon, wrong IP, firewalls, etc.).

The $k-session is totally useless, since you try to connect (again = 2nd parallel connection) to the private host from your local host, but not from the Cisco device. This explains the error described in the previous paragraph.

use Net::Cisco;
use Net::Telnet();
                                           # consider: use strict; 

$t =Net::Telnet::Cisco->new(Host=>'$ip');  # doesn't work: '$ip' -> $i
+p (BTW: where is $ip defined?)
print "connected";                         # a bold statement w/o any 
+test (e.g. checking $t)
$t->login('', '');
$t->cmd("telnet 192.168.201.3");           # failure? success? no chec
+k here
$k=Net::Telnet->new(Timeout=>10,Errmode=>'die'); 
                                           # You are opening a second 
+session from localhost!
                                           # Try to do the $k-stuff fr
+om within the $t-session.
$k->open("192.168.201.3")or die "$k->errmsg";
print "connected";                         # see above
$k->waitfor('password:$/i');
$k->print("public");
$k->waitfor('>$/i');
@output=$k->print("show system");
open(CONFIG,">config.txt");                # three argument open + che
+ck would be nice
print CONFIG "@output\n"; 
close(CONFIG);
$k->close;
$t->close;
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BTW: You can edit your nodes, e.g Reaped: telnet from a cisco telnet and do not need to create a new one when you want to update formatting or content.