Engaging the reader to generate emotions

Thank you for your question! I think the most important aspect of creating an emotional connection to a story and its characters is engagement. You engage the reader by

1. Appealing to their empathy -> We all know the guy in the movie who says “When this is all over I’m gonna go home and marry the love of my life” is gonna die, right? That one is a cliché at this point. But it still works in principle. It’s a variation on the “Save the Cat” idea, about making people sympathize with a character by showing them being sympathetic, be it by making them someone who saves a cat from a tree or by showing them as a character with significant connections and feelings. It all comes down to giving a character the background and personality traits that engage a readers empathy.
2. Making them relate -> Similarly to the point about empathy, it’s all about making a character sympathetic. They don’t have to be #relateable (if you know what I mean). A character is relateable when they are three-dimensional and their motivations, goals and flaws feel real. We can more easily root for them and be engaged and invested in their struggles.
3. Giving the character significant value -> Why do many comic relief characters tend to fall victim to a horrific death? Because a) this provides a significant juxtaposition to their personality, b) the death of laughter marks the story “getting serious” and c) they have an important function in the story and their absence is gonna be felt. This applies to any kind of character, not only the comic relief. It’s about creating characters that have a significant function in and add value to the story, so their absence, demise or otherwise cruel fate is creating a significant impact in the story itself and the other characters.

Writing this, I realize that most of my examples are about character death, but that’s not the only way you can make people feel sad about a character. Making and empathetic, engaging character is key to creating any emotional connection with the reader.

Hope this helps a bit. Have fun writing!