What Intel 4th gen processor will give you the same performance as a i3 6100

Solution
I'm not sure I understand, the i3 6100 is a fairly solid cpu for the price. There are several 4th gen cpu's that will outperform the i3 6100 but not at the roughly $115-120 price range of the i3. The 4690, 4690k, 4790, 4790k etc will outperform it but they're all upwards of $200 which contradicts 'budget'.
I'm not sure I understand, the i3 6100 is a fairly solid cpu for the price. There are several 4th gen cpu's that will outperform the i3 6100 but not at the roughly $115-120 price range of the i3. The 4690, 4690k, 4790, 4790k etc will outperform it but they're all upwards of $200 which contradicts 'budget'.
 
Solution
Why does it has to be a 4th gen CPU?
Are you running some benchmarks to compare against a i3-6100?

The i3-6100 is a hyperthreaded dual core running at 3.7 GHz.
The performance increase since SandyBridge were about 5-10% per generation.
for a comparable 4th generation chip look for a hyperthreaded dual core between 4 GHz and 4.4 GHz
Since no such chip exists you might want to look at an i5 instead.
I guess depending on the workload an i3 runs with around 80% the performance of a similar clocked i5 from the same generation. (just guesses, you might want to look at some benchmarks. But the differences between an i3 and i5 from the same generation are usually comparable)
Look for an i5 with around 3.2 - 3.6 GHz.
 
you can get q spec haswell chips that are better than the skylake & gives an i5 or i7 a run i picked up a i3 4340 Qspec for a haswell board the other day for $100 brand new l& these have turbo boost activated brings it from 3.6 to 3.7gh 4mb cache on par or better than any new gen around dont let these guys put you off the haswell i3s are prety solid have two built as gamers web browsers & prety much hack no issues they go as good or better than any i5 or i7 for next to nothing in price. I run i3s no issue havnt gone skylake & wont as not much in gain from the haswell to the skylake as more to go wrong in time with skylake even tho haswell is a dead chip i have 2 running on 2 stepsons set ups both over 3.5gh & over no issues on preformance runs & power these thing give i5 & i7 a real run for the $ they are so over rated try find a 4170 u wont have issues trust me i havnt yet