3 edited body
source | link
cnt = {};
i=0;                                        (*added*)
CreateWindow[DialogNotebook[{
   "Click on ADD button to add more cells:",
   Dynamic@Column@cnt,
   Button["ADD", 
   i++;                                     (*added*)
   nm=ToExpression["a"<>ToString@i];        (*added*)
   AppendTo[cnt, 
    InputField[Dynamic@Evaluate@nm,         (*updated*)
               FiledHintFieldHint->"Enter new input here"]]]   
   }, WindowSize -> 250, 
  WindowElements -> {"VerticalScrollBar", "StatusArea"}]]

enter image description here

The array of inputfields stores data in specially created variables a1, a2,....ax.

cnt = {};
i=0;                                        (*added*)
CreateWindow[DialogNotebook[{
   "Click on ADD button to add more cells:",
   Dynamic@Column@cnt,
   Button["ADD", 
   i++;                                     (*added*)
   nm=ToExpression["a"<>ToString@i];        (*added*)
   AppendTo[cnt, 
    InputField[Dynamic@Evaluate@nm,         (*updated*)
               FiledHint->"Enter new input here"]]]   
   }, WindowSize -> 250, 
  WindowElements -> {"VerticalScrollBar", "StatusArea"}]]

enter image description here

The array of inputfields stores data in specially created variables a1, a2,....ax.

cnt = {};
i=0;                                        (*added*)
CreateWindow[DialogNotebook[{
   "Click on ADD button to add more cells:",
   Dynamic@Column@cnt,
   Button["ADD", 
   i++;                                     (*added*)
   nm=ToExpression["a"<>ToString@i];        (*added*)
   AppendTo[cnt, 
    InputField[Dynamic@Evaluate@nm,         (*updated*)
               FieldHint->"Enter new input here"]]]   
   }, WindowSize -> 250, 
  WindowElements -> {"VerticalScrollBar", "StatusArea"}]]

enter image description here

The array of inputfields stores data in specially created variables a1, a2,....ax.

2 updated according to comments
source | link
cnt = {};
i=0;                                        (*added*)
CreateWindow[DialogNotebook[{
   "Click on ADD button to add more cells:",
   Dynamic@Column@cnt,
   Button["ADD", 
   i++;                                     (*added*)
   nm=ToExpression["a"<>ToString@i];        (*added*)
   AppendTo[cnt, InputField["Enter
    InputField[Dynamic@Evaluate@nm,         (*updated*)
               FiledHint->"Enter new input here"]]]   
   }, WindowSize -> 250, 
  WindowElements -> {"VerticalScrollBar", "StatusArea"}]]

enter image description here

The array of inputfields stores data in specially created variables a1, a2,....ax.

cnt = {};
CreateWindow[DialogNotebook[{
   "Click on ADD button to add more cells:",
   Dynamic@Column@cnt,
   Button["ADD", AppendTo[cnt, InputField["Enter new input here"]]]
   }, WindowSize -> 250, 
  WindowElements -> {"VerticalScrollBar", "StatusArea"}]]

enter image description here

cnt = {};
i=0;                                        (*added*)
CreateWindow[DialogNotebook[{
   "Click on ADD button to add more cells:",
   Dynamic@Column@cnt,
   Button["ADD", 
   i++;                                     (*added*)
   nm=ToExpression["a"<>ToString@i];        (*added*)
   AppendTo[cnt, 
    InputField[Dynamic@Evaluate@nm,         (*updated*)
               FiledHint->"Enter new input here"]]]   
   }, WindowSize -> 250, 
  WindowElements -> {"VerticalScrollBar", "StatusArea"}]]

enter image description here

The array of inputfields stores data in specially created variables a1, a2,....ax.

1
source | link

cnt = {};
CreateWindow[DialogNotebook[{
   "Click on ADD button to add more cells:",
   Dynamic@Column@cnt,
   Button["ADD", AppendTo[cnt, InputField["Enter new input here"]]]
   }, WindowSize -> 250, 
  WindowElements -> {"VerticalScrollBar", "StatusArea"}]]

enter image description here