The effect varies for everyone but a traditional combined contraceptive pill i.e one that contains estrogen/oestrogen and not progestrone only will commonly have some effect (also oestrogen based implants and injections). The minority escape supply issues. Lactation can only be easily maintained when oestrogen is naturally lowered
especially if your baby is young. This is one of the reasons supply often decreases when people fall pregnant. It's not recommended to take the combined pill at all if your baby is under 6 months and after then you should be very cautious and consider other methods if breastfeeding is something you'd like to maintain without risk.
Kellymom list tri-cyclene as an L3 category - 'moderately safe' for lactation but there are L2 category available which are even safer (although risk to supply cannot to ruled out). So tri-cyclene is actually one of the more riskier available:
http://www.kellymom.com/health/meds/birthcontrol.htmlljed78 if your baby is younger than 6 months I would suggest you reconsider - if older, then you could risk it but monitor carefully.