We're in the "Travelling to the USA" section so I guess it's the USA.
The US takes an extreme approach to anyone on the SOR, even more than the UK.
I would advise not travelling to the US while on the SOR. For any non-EU and non-Schengen travel, the police can issue an Interpol Green Notice when you notify travel (they won't tell you whether they have or not). If there is a Green Notice on you, this will flag up on arrival and you will be deported to the UK, possibly after being detained.
You could lie on the ESTA, but if you are notifying travel under the SOR then they might tell the US anyway.
I would guess a visa application for the US would be almost immediately rejected for anyone convicted of a sex offence, given their stance.
Honestly I would abstain from any travel to the US until you're no longer on the SOR, then I would get an ESTA and tick "no" to the infamous question.
The US does not have access to the UK Police National Computer - they can only do so by making an individual request, and only then if they have grounds for suspicion, not as part of a random check. So once you've finished on the SOR and have been able to travel to other countries without being pulled aside, I would go for it with the US on an ESTA.
On the other hand, a visa decision can be appealed, while an ESTA rejection cannot. Visa application is the legally correct way to go, but perversely the less likely way to get in!
I have travelled to non-EU, non-Schengen countries while on the SOR with no problem, but the US is not one of them.