How to convince a customer of an offer or service when it doesn't match his inquiry?

talk politely and try to find out the intention of the customer and try to give the introduction of the goods which are there in your install from which he/she may be impressed.

It is all about added value.
Qualifying the customer needs comes first.
Then proposing value and not a product or service.
If you show the customer the value added to his business from the product or service then your product sells itself.
Features+Benefits=Value.
Focus on the features being very careful to illustrate benefits, that will show value.
Do this only after qualifying the customer needs.
Give them what they want and more so you get what you want :)

since your customer doesn't "need" your service, but he might "take it" if you convince him.
then find his weakness point, and start from there.
you can embrace him or flatter him or dazzle him in a way or another!! if he is so smart try to increase the benefits and lower the price..that's what smart people seek

1-Adjust Your Mindset: (All that matters is that you realize that your customer or client is upset, and that it's up to you to solve the problem.
Adjust your mindset so that you're giving100 percent of your focus to your client, and to the current situation.
)
2- Listen Actively: (Don't allow anything to interrupt this conversation.
Give your client all of your attention.
)3-Repeat Their Concerns: (you agree on the problem that needs to be solved.)4-Be Empathic and Apologize: (you could say, "I understand why you're upset.
I would be too.
I'm very sorry that we didn't get the samples to you on time, especially since it's caused these problems." )5-Present a Solution: (you could say, "If my solution doesn't work for you, I'd love to hear what will make you happy.
If it's in my power I'll get it done, and if it's not possible, we can work on another solution together." -6-Take Action and Follow-up: (Once the situation has been resolved, follow up with your client over the next few days to make sure that she's happy with the resolution.
Whenever you can, go above and beyond her expectations.
For instance, you could send her a gift certificate, give her a great discount on her next purchase, or send her a hand-written apology.
)7-Use the Feedback: (our last step is to reduce the risk of the situation happening again.
If you haven't already done so, identify how the problem started in the first place.
Was there a bottleneck that slowed shipment? Did a sales rep forget to confirm an order?

I will try to explain very well in order to convince him that our product is suitable for his need.

Try to explain that your product can suit his needs and perform better than his expectations.
let him know about your after sales service plan.
give him a reminder call if required.

there are many ways to convnce a customer , btwe hv to select da most proper way and da most appropraite....
if his inquiry doesnt match,dn v hv to cnvince hm wid alternation optionsor altrnate offers,1st condition is tht b careful abt da communication skill da most soft tone shud b use toward da customer, f still thr is a prob dn da aplogizing tone shud b use like : im sorry to say tht we do not offr ds service, or im very sory fr da incnvinience ...
bla bla bla ...........
da most important is communication skill n bear da criticism :)

From my side I will not offer something will not bring value to the customer, if i do how the customer will come back to me for more business, I need to know his problem and provide the solution for him as per his requirements

Listen to him carefully.
Once the level of listen and trusting is building, you recommend him your offer and how it will benefit him.
Also add some goodies along.