One example, and perhaps the most convincing example, of psychologists, including neuroscientists, actually concluding from their research that a standard mental event is best understood as, literally, an illusion that people have is the frequent scientific conclusion that our belief that we have free will is an illusion.
Here is one good example of how the term "free will" itself is usually defined in this context:
"Free will may be defined as an agent's ability to act on the world by its own volition, independently of purely physical (as opposed to metaphysical) causes and prior states of the world"
(definition used in the context of a debate specifically on free will organised by the Society for Personality and Social Psychology).
I don't think this definition makes any sense, but it seems clear that we nonetheless standardly have something like a very strong belief that we can very often, indeed routinely, do exactly what we wanted to do.
As an example, suppose you are asked to take part in a poll where the question is whether you think you have free will or you think you don't (plus options such as "Don't know" etc.).
I would certainly expect most people to choose to vote that they think they have free will. However, this is not the point. The point is that you are presented with a choice and that whatever your vote will be you do something which will be deemed to be the expression of your choice.
There seems to be little point in denying that you would indeed express your choice and do what you actually wanted to do in selecting whatever option you would.
It also seems beyond controversy that most people in that sort of situation don't spend a long time considering and deliberating with themselves, i.e. consciously, their possible answer. Thus, I think we can assume that, very often, people make their choice without consciously deliberating what choice to make. Thus, we can take what they come to want to do in this context to be essentially the result of an unconscious process.
Obviously, there are many situations where we do deliberate with ourselves hard and long before electing to perform a particular action. However, this is irrelevant here. The fact seems to be that most of the things we do in life, including voting, something which is taken to be the means to express the will of the people, are done without any rational, and therefore conscious, deliberation.
Yet, in many such situations, we will indeed believe that we will have done what we wanted to do, which I think is really the point of free will.
In this example, we have on one side a strong belief, that we can often, routinely, do what we want, and on the other the scientific contention, by psychologists, that free will is best understood, literally, as an illusion.
This, however, clearly does not amount to anything like our brain tricking us into having the illusion that we are acting according to our free will.
What we routinely believe is, literally, that we are doing what we want at the moment. Scientific studies don't deny that we do want something on these occasions. They also don't deny that we end up actually doing what we so wanted to do.
What scientific studies seem to be concluding is that free will as defined above, what I call a metaphysical definition of free will, is an illusion. However, they don't actually prove, they don't even try to prove, that we really have this metaphysical belief to begin with, as opposed to just believing, however strongly, that you can often, routinely, do what you want.
Thus, I don't think there is any substance to the notion that the brain is literally tricking us into thinking anything. Clearly, our brain makes us for example want to do things and that this somehow seems to make us do or try to do it. This, however, doesn't amount to anything like a "trick".
Otherwise, you might just as well take our perception of the world around us to be a trick of the brain to make us believe that there is a particular kind of material world out there even though there isn't in fact such a world.
More likely, we should take any suggestion that our brain tricks us as literary licence. In other words, the only trick here is other people trying to trick you into believing meaningless headlines.
Here is an example of such a headline:
Brain Tricks Us Into Thinking We Are In Control
(From PsyBlog, a website founded and authored by Psychologist, Jeremy Dean, PhD in psychology from University College London, MSc in Research Methods in Psychology and a Post Graduate Diploma in Psychology. https://www.spring.org.uk/2016/05/free-will-is-an-illusion.php)
And here is one claim fleshing out the headline:
"While it may feel like we are in control of our actions, this is just a fantasy our brain creates so we don’t feel left out."
So, there is undoubtedly a cottage industry of psychologists making the brain-tricks-us claim again and again, both literally, in their "headlines", and in the substance of what they say in support of the headline.
When it comes to actual scientific papers, however, it seems very hard to find any example of the claim itself. The word "trick" is indeed very often used in the context of the neurosciences but, as far as I can tell, it is essentially either to express the idea that the brain performs very remarkable cognitive feats, or used as shorthand for new abilities that the brain can be taught to develop.
So, maybe, don't let the cottage industry of psychologists trick you into believing real science makes any claim that your brain tricks you in any way.