Firstly: 

Nicotine is a natural substance which is alkaline and toxic. It is regarded as one of the most dangerous of harmful substances to be found in tobacco, and it is the substance that causes addiction in smokers. Hence scientists have tried hard to come up with alternatives that will help the smoker to rid himself of the harmful addiction to nicotine by manufacturing a lighter version of nicotine in the form of pills, chewing gum or sticks like cigarettes, or patches containing varying amounts of nicotine, to introduce the smoker gradually to alternatives, so that he will be able to stop smoking for the longest possible period, without having to face the effects of withdrawal that would result from stopping smoking suddenly, which usually makes the smoker go back to smoking in order to free himself from these withdrawal symptoms. 

Secondly: 

The nicotine patch is like a sticker which releases nicotine in the form of a gel which is absorbed by the skin, and the nicotine then passes via the capillaries into the bloodstream, and helps the smoker to avoid withdrawal symptoms. There are three types of nicotine patches, based on the strength of their effects, 5 mg, 10 mg and 15 mg. The patch is usually applied to the upper arm, where it remains for 16 hours of the day, and it is not used when sleeping. There may be some harmful side effects such as irregular heartbeat, nausea and overall weakness. 

Thirdly: 

With regard to the ruling on using it, it is permissible in sha Allaah, but if it leads to harmful effects then it is not permissible in that case. It depends on the advice of a trustworthy doctor. 

If a person uses them whilst fasting, that does not affect his fast. 

It says in a statement of the Islamic Fiqh Council (no. 93): 

The following things are not regarded as breaking the fast … among which they listed: 

Whatever enters the body through the skin, such as creams, ointments and skin patches containing medicines or chemicals. End quote. 

Shaykh Muhammad ibn Saalih al-Uthaymeen (may Allaah have mercy on him) was asked: 

Some pharmacies sell medical patches which are placed on the body and give the body what it needs of nicotine for twenty-four hours, as a step towards giving up smoking. 

My question is: If it is put on at night for twenty-four hours, then another one is put on, is a person breaking the fast in Ramadaan if he uses that? 

He replied: 

He is not breaking the fast in Ramadaan, and he may use them. In fact it may be obligatory for him to use them if this is a way of stopping smoking. There is nothing wrong with a person giving up something haraam gradually, because when Allaah wanted to forbid alcohol, He did not forbid it outright in one go, rather He did it gradually. He permitted it at first, then He pointed out that its harmful effects were greater (than any benefits), then He forbade it at some times, then He forbade it altogether. These four stages were as follows: 

1-

He permitted it in the verse (interpretation of the meaning): 

“And from the fruits of date palms and grapes, you derive strong drink and a goodly provision”

[al-Nahl 16:67]

This is in the context of reminding them of His blessings, so it was permitted.  

2-

He hinted that it was forbidden in the verse (interpretation of the meaning):  

“They ask you (O Muhammad صلى الله عليه وسلم) concerning alcoholic drink and gambling. Say: ‘In them is a great sin, and (some) benefits for men, but the sin of them is greater than their benefit’”

[al-Baqarah 2:219]

3-

He forbade it at certain times: 

“O you who believe! Approach not As‑Salaah (the prayer) when you are in a drunken state”

[al-Nisa’ 4:43]

This means that one should not drink when one is going to pray.  

4-

He forbade it altogether in the verse (interpretation of the meaning): 

“O you who believe! Intoxicants (all kinds of alcoholic drinks), and gambling, and Al‑Ansaab (stone altars for sacrifices to idols etc), and Al‑Azlaam (arrows for seeking luck or decision) are an abomination of Shaytaan’s (Satan’s) handiwork. So avoid (strictly all) that (abomination) in order that you may be successful”

[al-Maa'idah 5:90]. 

When the prohibition on alcohol was revealed, the vessels of the Sahaabah were full of wine, but they took them out into the marketplace and emptied them out. Glory be to Allaah, what is the difference between us and them? The difference between us and them in following commands is like the difference between their time and our time.  They did not hesitate; they did not say we will drink up what is left in the vessels. Not at all. They were drinking together, and they went and poured it out in the marketplaces. They gave it up altogether, and they did not say: We are accustomed to this, or any such thing. No, they gave it up altogether, because they had the resolve that made it easy for them to face hardships. 

Al-Jalasaat al-Ramadaaniyyah (1415 AH, 1/question no. 10). 

Fourthly: 

There is nothing wrong with praying with the patch on one's body, because it does not contain any impurity (najaasah) that could affect the validity of his prayer. It is also placed on the upper arm, which is a part of the body that does not need to be washed when doing wudoo’. 

But it must be removed if one wants to do ghusl from janaabah. 

We ask Allaah to help you to give up this filthy haraam habit. 

And Allaah knows best.