It’s a between-subject design with a control group and a treatment group with 50 people each. Each participant undergoes 100 trails. (repeated measures). So the only within-subject factor is the number of trails. The independent variable is dummy coded (0 & 1). The dependent variable is continuous,it varies between [3.00 to 6.00].I want to compare the means between the two. Should I use a repeated-measures ANOVA / mixed model / T-test/MANOVA?
What is a good approach and why?

I understand that, I can have a mixed model and find anova for that.Is this right?

As this is more of a basic stats question, I think in future you might get a more rapid answer over at stats.stackexchange.com.

To answer your question, the data you describe are structured hierarchically (many observations nested within each of many individuals), so you would want to use a hierarchical (a.k.a. mixed effects) model that includes a parameter that encodes the difference between the control and treatment groups’ respective means.

Welcome to the forum!
Just to be clear, I think most people here believe that for the kind of analysis you have in mind, Bayesian analysis, using a mixed model, with packages based on Stan (most likely rstanarm , possibly brms ) are the best you can get. For such use cases we also provide support here. Depending on the exact scientific question you have, it is likely most people here would also advise you against doing a “test” with a yes/no answer and instead just try to estimate the effect size and its associated uncertainty. If you absolutely have to, you might want to do a hypothesis test with a Bayes factor using the bridgesampling package, but Bayes factors may be tricky to get right (I’ve never used them myself, just know this is what people I respect say about them).

We will be able to help you most effectively, if you include more information about your ultimate scientific question (the “big picture”) and what exactly are your dependent and independent variables and how are they measured.

Unfortunately, if you, for whatever reason, want/need to stay within a frequentist framework (p-values, ANOVA, …), that would be outside the scope of this forum and we would ask you to move your question elsewhere. Even though I sympathize that getting an answer on Cross Validated is hard (I think I never got one unless I put a bounty on the question).

Stan isn’t exclusively a Bayesian package. Stan also fits (penalized) maximum likelihood estimates. RStan even provides standard errors based on Hessian approxiamtions. And I’m writing a new chapter in the user’s guide on how to compute bootstrap estimates of variance and confidence intervals.

Having said that, it’s not what Stan’s typically used for.

You are absolutely right and I made my statement unnecessarily strict, sorry @amini for that, frequentist stats run with the help of Stan are definitely on-topic.