I'm not sure specifically as I haven't read this fanfic. But generally, if Harry is related to the TARDIS in a fanfic, it might involve some sort of crossover where Harry from the Harry Potter universe has an encounter or connection with the TARDIS from Doctor Who. It could be a really creative take on combining two very different fictional worlds.
Well, in the 'harry built the tardis fanfic', first of all, it's a really cool concept. Harry is known for his adventures in the wizarding world, and the TARDIS is such an iconic part of Doctor Who. The fanfic might start with Harry stumbling upon some ancient plans or technology that gives him the idea to build the TARDIS. He could face many challenges, like getting the right materials. And once he starts building, he might have to deal with the magical and scientific aspects that don't quite match up in the normal sense. It could be a story full of discovery, adventure, and the combination of two very different fictional universes.
One main idea could be the combination of different fictional universes. Harry from one and the TARDIS from another.
Since I don't have first - hand knowledge of this fanfic, my best guess is that it could involve a situation or concept that is more 'blue' in nature compared to the TARDIS. Maybe it has to do with a different kind of blue - hued alien or a blue - tinted dimension that is explored in the story. It could also be a play on words, where 'bluer' refers to something other than the color, like a 'bluer' state of mind, and the story then weaves this concept in relation to the TARDIS, perhaps showing how this 'bluer' thing interacts with or is different from the TARDIS.
You could try searching on popular fanfic websites like Archive of Our Own (AO3) or FanFiction.net. These platforms usually have a large collection of fanfics, and you might be able to find this particular one by using the title or relevant tags in the search bar.
I haven't actually read this fanfic. But generally, it might be about Harry from the Harry Potter universe building a TARDIS which is from Doctor Who. It could involve him using his magic skills to construct this time - and - space - traveling device. Maybe he combines spells from Hogwarts with the technology (in a magical way) of the TARDIS.
Probably the moment when Harry actually makes the TARDIS work. It's like seeing two different fictional universes collide in a functional way.
The concept of time is also treated differently in this type of fanfiction. While the Time - Turner in Harry Potter allows for a limited form of time travel, the TARDIS can travel through all of time and space. Fanfiction writers often explore how these two different time - traveling mechanisms interact. They might have the TARDIS enhance the power of the Time - Turner or use the Time - Turner to fix a problem within the TARDIS's time - space continuum. This exploration of time adds a whole new layer of complexity and uniqueness to the stories.
The Tardis site of Fanfiction.net offers many types of Harry Potter fanfics. There are those that continue the story after the original series ended, and some that reimagine key moments. You could also find crossovers with other popular franchises.
Yes, there are likely some fanfictions out there with this concept. Fanfiction writers often come up with creative crossovers, and combining the magical world of Harry Potter with the time - and - space - traveling TARDIS from Doctor Who is a really interesting idea that some fans might have explored in their writing.
One interesting plotline could be Clara discovers a hidden chamber inside the TARDIS that contains secrets about the Doctor's past. Maybe it holds memories or artifacts that the Doctor has long forgotten or tried to keep hidden.