iterate data from multiple json files using cypress

The it method needs to be directly inside the describe method (see https://docs.cypress.io/guides/getting-started/writing-your-first-test#Write-your-first-test)

describe('My First Test', () => {
  it('Does not do much!', () => {
    expect(true).to.equal(true)
  })
})

Which in your case would give something like:

const studList = require('../../fixtures/studDetails.json')

describe('Get Student Details', function() {
    it('Login Test', function() {
        // filter list to get only the "English" students
        const targetStudents = studList.filter(stud => stud.StudentDept === "English");

        if(targetStudents.length === 0) {
            // do not test if no result
            console.log("Didn't find any student to test with.");
            return;
        }

        for(const stud of targetStudents) {
            let studentId = stud.StudentId;
            let studentName = stud.StudentName;
            let studDept = stud.StudentDept;

            const deptList = require('../../fixtures/' + studDept + '.json');

            for(const dep of deptList) {
                let deptLead = dept.LeaderName;
                let deptController = dept.Controller; 

                cy.visit('http://localhost:8081/login/');
                cy....
                cy....
                cy.get('#deptHead1').set(deptLead);
                cy.get('#deptHead2').set(deptController);
            }
        }
    });
});

Your code looks right to me. I'm not sure what your department JSON contents may be, but this is what I used and got it to work.

studentDetails.json

[
    {
        "StudentId": "1001",
        "StudentName": "Tim Blanks",
        "StudentDept": "English"
    },
    {
        "StudentId": "1002",
        "StudentName": "Alec Stoinis",
        "StudentDept": "Physics"
    },
    {
        "StudentId": "1003",
        "StudentName": "Fiona Woods",
        "StudentDept": "English"
    }
]

English.json

[
    {
        "DepartmentId": "1001",
        "DepartmentName": "English",
        "DepartnmentLeader": "MrsJohson",
        "DepartmentController": "TheDarkLord"
    }
]

test.js

const studentList = require('../fixtures/studentDetails.json')

describe('Get Student Details', function () {
    studentList.forEach(student => {
        const studentDept = student.StudentDept
        if (studentDept == 'English') {
            const departnmentJSON = require(`../fixtures/` + studentDept + `.json`)
            departnmentJSON.forEach(department => {
                const deptLead = department.DepartnmentLeader
                const deptController = department.DepartmentController

                it(`${department.DepartmentName} department`, () => {
                    cy.log(deptLead)
                    cy.log(deptController)
                    // real test code here
                })
            })
        }
        // code for other departments
    });
})

You must remove the describe().

Inside describe(), Cypress does not evaluate studList.forEach(stud => { or deptList.forEach(dept => { until test runs, so it sees no tests.

Outside describe() studList.forEach(stud => { and deptList.forEach(dept => { are run as part of test setup, now Cypress knows how many tests you have.

const studList = require('../../fixtures/studDetails.json')

studList.forEach(stud => {    
        
  let studentId = stud.StudentId;
  let studentName = stud.StudentName;
  let studDept = stud.StudentDept;

  if (studDept === "English") {
    const deptList = require('../../fixtures/'+ studDept +'.json');
    deptList.forEach(dept => {
      let deptLead = dept.LeaderName;
      let deptController = dept.Controller;  
                
      it(`Login Test for Student ` + studentName , function() {
        cy.visit('http://localhost:8081/login/');
        ....
      })

      it('Grades test for ' + deptController, function() {
        cy.visit('http://localhost:8081/login/');
        ....
      })

    })
  }    
})

Or put it here

const studList = require('../../fixtures/studDetails.json')

studList.forEach(stud => {    
        
  let studentId = stud.StudentId;
  let studentName = stud.StudentName;
  let studDept = stud.StudentDept;

  if (studDept === "English") {
    const deptList = require('../../fixtures/'+ studDept +'.json');
    deptList.forEach(dept => {
      let deptLead = dept.LeaderName;
      let deptController = dept.Controller;  

      //Use describe here                
      describe('Get Student Details', function() {

        it(`Login Test for Student ` + studentName , function() {
          cy.visit('http://localhost:8081/login/');
          ....
        })

        it('Grades test for ' + deptController, function() {
          cy.visit('http://localhost:8081/login/');
          ....
        })
      })
    })
  }    
})