I've got what I believe to be 3 Chicago Hardy  trees (first year) in pots outside.   They all have lots of figs on them, but the figs have been green and not grown for quite some time. 

When should I expect them to begin ripening?  

Most of the figs have stunted (about a month or more) but the tree keeps producing smaller, new ones.  Is it true that these small, new ones prevent the rest from ripening?  If so, is it best to cut the small ones so the others that have been there for a while ripen?

Or, as is most likely the case, do I just need to be more patient and wait till fall for them to ripen?  I just seem to remember that the tree these clippings came from were good to go by now, but then again, the tree was in the ground. 

Yes it is true the new one prevent the older ones from ripening.
Take the new ones off,ASAP,if you want ripe fruits.

How old are the plants?

How long ago did you see the first little figs?  Can take 90 to 120 days from then to ripen.  I have two plants, celeste and a BT which have been producing ripe figs for the last 2 weeks.   

Having said that, Weather in NJ looks great over next 10 days.  Lots of sunny warm days.  Be patient.  When the figs start to turn they will ripen fast.  Also, I harvest figs here in NJ from one late plant well into mic October.  Lots of time left.

These plants are one year old, almost to the day.  I clipped them from the original tree last year, they rooted around Oct, then grew them inside all winter.  

I put them outside in May and started to see figs in July.  

I took Herman2's advice and removed all the small ones.   Is there any chance these little ones will become edible if I leave them out on the counter?  Seems like such a waste to throw them out.

   

No Chance
Edit note:I got ripe fruits ,from following trees started Aug 21:
Improved Celeste,Ronde De Bordeaux,Saint Anthony,Malta Black,Maltese Falcon,all growing in ground.
I am north/east of Philadelphia about 10 miles.

I heard some varieties can ripen on a broken off branch, but with no branch?

Theres are good jam recipe cor unripe figs.

I haven't harvested any ripe figs yet from my trees in NJ, but they are starting to go now. Celeste, Sicilian, Petite Negri, Negronne, Vista, and Chicago Hardy are on their way. With all the hot weather, I was wondering myself when they'd start to ripen.

If you started to see the first figlets in early July, then for Chicago Hardy I think the soonest the figs would be ripe would be late Sept or early Oct. 

My earliest ripening fig this year was my fabulous RdB that I received from Vasile 2 years ago. Also his Black Malta (2nd. year from a cutting) has given  me a bunch so far. My Dominicks have been at it for at least a week or so already as has Atreano (thanks Vito and Art) A TC VdB that is in its 3rd year has also started a week or so ago and there are tons of figs on it. This is my first Tissue Culture plant from Wellspring. Really excellent results on a plant that wasnt even pencil sized when I got it.
All are in pots

It's quite interesting to see different growers experiences with ripening in the same area but with the same varieties ripening at different times.  For potted plants, I would think it should depend upon how figs are stored for the winter and therefore when the plants break hibernation and when the potted figs are placed outdoors.  However, mine went outside 2 weeks later than last year and my figs ripened just about the same time so perhaps this is not the case.  I would think age of the plant may have something to do with it too and the pots they are in.  Lastly perhaps it's how much sun they receive.  Mine get close to 8 hours with full sun during the mid day.  

Anybody else have some knowledge on this question or care to speculate!

Does watering have anything to do with it?  I've been watering mine everyday because if I don't they wilt during the day - I believe this is due to the excessive heat we've been having (90 degree plus). 

But wonder if less water ripens faster?