Southpaws(a left handed fighter who jabs with the right hand) will always present a tricky challenge to an orthodox fighter(someone who jabs with the left hand and is essentially right handed) as the majority of fighters are right handed, so whereas the southpaw is used to fighting orthodox boxers, the orthodox boxer wont have come across southpaws as much so from the start, the southpaw at least has this advantage of familiarity.
The video below contains a number of tips you can effectively use against a southpaw, the first and most important rule is to ensure you have outside lead foot positioning over the southpaw, make sure your lead foot is on the outside of the southpaws, this helps you to slip outside of his jab and counter with your right hand, the right hand is going to be your most important hand against a southpaw due to the angles involved.
Don’t try to out jab the southpaw, jab at their gloves, short and hard, and throw right hand lead off your jab to their gloves. Once you’ve got the lead right hand going and the southpaw is conscious of this, feint the right hand and throw the lead left hook, mix it up, jabs to gloves, lead right hand, lead left hook.
My favourite counter to a southpaws jab is the right hand to the body, follow up with the left hook to the head for increased effectiveness. You can also counter the jab with a right to the head, something Floyd Mayweather Jnr was extremely good at. If you want to counter their jab with your own jab, then parry the jab and come straight over the top with your own jab.
*Bonus Tip – Not included in this video is the lead right hand followed by the check hook, so throw the right cross at the southpaw, and then pivot whilst throwing the left hook to the head.