[Vuejs]-How to pass data from a parent blade to a included modal?

You can use $emit method for this purpose.
v-on directive captures the child components events that is emitted by $emit

Child component triggers clicked event:

export default {
  methods: {
    onClickButton (event) {
      this.$emit('clicked', 'someValue')
    }
  }
}

Parent component receive clicked event:

<div>
  <child @clicked="onClickChild"></child>
</div>

export default {
  methods: {
    onClickChild (value) {
      console.log(value) // someValue
    }
  }
}